Search results for: autocorrelated kernel density estimator

Authors: Fekadu L. Bayisa, Elvan Ceyhan, Todd D. Steury

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Interaction between individuals within the same species is an important component of population dynamics. An interaction can be either static (based on spatial overlap) or dynamic (based on movement interactions). Using GPS collar data, we can quantify both static and dynamic interactions between black bears. The goal of this work is to determine the level of black bear interactions using the 95% and 50% home ranges, as well as to model black bear spatial interactions, which could be attraction, avoidance/repulsion, or a lack of interaction at all, to gain new insights and improve our understanding of ecological processes. Recent methodological developments in home range estimation, inhomogeneous multitype/cross-type summary statistics, and envelope testing methods are explored to study the nature of black bear interactions. Our findings, in general, indicate that the black bears of one type in our data set tend to cluster around another type.

Keywords: autocorrelated kernel density estimator, cross-type summary function, inhomogeneous multitype Poisson process, kernel density estimator, minimum convex polygon, pointwise and global envelope tests

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Authors: Abdel-Razzaq Mugdadi, Ruqayyah Sani

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The Kernel Distribution Function Estimator (KDFE) method is the most popular method for nonparametric estimation of the cumulative distribution function. The kernel and the bandwidth are the most important components of this estimator. In this investigation, we replace the kernel in the KDFE with a linear combination of kernels to obtain a new estimator based on the linear combination of kernels, the mean integrated squared error (MISE), asymptotic mean integrated squared error (AMISE) and the asymptotically optimal bandwidth for the new estimator are derived. We propose a new data-based method to select the bandwidth for the new estimator. The new technique is based on the Plug-in technique in density estimation. We evaluate the new estimator and the new technique using simulations and real-life data.

Keywords: estimation, bandwidth, mean square error, cumulative distribution function

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Authors: R. Sabre, W. Horrigue, J. C. Simon

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This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.

Keywords: spectral density, stable processes, aliasing, periodogram

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Authors: Benson Ade Eniola Afere

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Over the years, kernel density estimation has been extensively studied within the context of nonparametric density estimation. The fundamental components of kernel density estimation are the kernel function and the bandwidth. While the mathematical exploration of the kernel component has been relatively limited, its selection and development remain crucial. The Mean Integrated Squared Error (MISE), serving as a measure of discrepancy, provides a robust framework for assessing the effectiveness of any kernel function. A kernel function with a lower MISE is generally considered to perform better than one with a higher MISE. Hence, the primary aim of this article is to create kernels that exhibit significantly reduced MISE when compared to existing classical kernels. Consequently, this article introduces a cluster of hybrid polynomial kernel families. The construction of these proposed kernel functions is carried out heuristically by combining two kernels from the classical polynomial kernel family using probability axioms. We delve into the analysis of error propagation within these kernels. To assess their performance, simulation experiments, and real-life datasets are employed. The obtained results demonstrate that the proposed hybrid kernels surpass their classical kernel counterparts in terms of performance.

Keywords: classical polynomial kernels, cluster of families, global error, hybrid Kernels, Kernel density estimation, Monte Carlo simulation

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Authors: R. Sabre

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This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.

Keywords: spectral density, stable processes, aliasing, non parametric

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Authors: Hung-Sheng Lin, Cheng-Hsuan Li

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Over the past few years, kernel-based algorithms have been widely used to extend some linear feature extraction methods such as principal component analysis (PCA), linear discriminate analysis (LDA), and nonparametric weighted feature extraction (NWFE) to their nonlinear versions, kernel principal component analysis (KPCA), generalized discriminate analysis (GDA), and kernel nonparametric weighted feature extraction (KNWFE), respectively. These nonlinear feature extraction methods can detect nonlinear directions with the largest nonlinear variance or the largest class separability based on the given kernel function. Moreover, they have been applied to improve the target detection or the image classification of hyperspectral images. The double nearest proportion feature extraction (DNP) can effectively reduce the overlap effect and have good performance in hyperspectral image classification. The DNP structure is an extension of the k-nearest neighbor technique. For each sample, there are two corresponding nearest proportions of samples, the self-class nearest proportion and the other-class nearest proportion. The term “nearest proportion” used here consider both the local information and other more global information. With these settings, the effect of the overlap between the sample distributions can be reduced. Usually, the maximum likelihood estimator and the related unbiased estimator are not ideal estimators in high dimensional inference problems, particularly in small data-size situation. Hence, an improved estimator by shrinkage estimation (regularization) is proposed. Based on the DNP structure, LDA is included as a special case. In this paper, the kernel method is applied to extend DNP to kernel-based DNP (KDNP). In addition to the advantages of DNP, KDNP surpasses DNP in the experimental results. According to the experiments on the real hyperspectral image data sets, the classification performance of KDNP is better than that of PCA, LDA, NWFE, and their kernel versions, KPCA, GDA, and KNWFE.

Keywords: feature extraction, kernel method, double nearest proportion feature extraction, kernel double nearest feature extraction

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Authors: O. Abiodun Adeyinka, B. Adeyemo Adesesan

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The forensic use of handwriting depends on the analysis, comparison, and evaluation decisions made by forensic document examiners. When using biometric technology in forensic applications, it is necessary to compute Likelihood Ratio (LR) for quantifying strength of evidence under two competing hypotheses, namely the prosecution and the defense hypotheses wherein a set of assumptions and methods for a given data set will be made. It is therefore important to know how repeatable and reproducible our estimated LR is. This paper evaluated the accuracy and reproducibility of examiners' decisions. Confidence interval for the estimated LR were presented so as not get an incorrect estimate that will be used to deliver wrong judgment in the court of Law. The estimate of LR is fundamentally a Bayesian concept and we used two LR estimators, namely Logistic Regression (LoR) and Kernel Density Estimator (KDE) for this paper. The repeatability evaluation was carried out by retesting the initial experiment after an interval of six months to observe whether examiners would repeat their decisions for the estimated LR. The experimental results, which are based on handwriting dataset, show that LR has different confidence intervals which therefore implies that LR cannot be estimated with the same certainty everywhere. Though the LoR performed better than the KDE when tested using the same dataset, the two LR estimators investigated showed a consistent region in which LR value can be estimated confidently. These two findings advance our understanding of LR when used in computing the strength of evidence in handwriting using forensics.

Keywords: confidence interval, handwriting, kernel density estimator, KDE, logistic regression LoR, repeatability, reproducibility

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Authors: Wen Liu

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With the rapid progress of modern cities, the railway construction must be developing quickly in China. As a typical high-density country, shopping center on the subway should be one important factor during the process of urban development. The paper discusses the influence of the layout of shopping center on the subway, and put it in the time and space’s axis of Shanghai urban development. We use the digital technology to establish the database of relevant information. And then get the change role about shopping center on subway in Shanghaiby the Kernel density estimate. The result shows the development of shopping center on subway has a relationship with local economic strength, population size, policy support, and city construction. And the suburbanization trend of shopping center would be increasingly significant. By this case research, we could see the Kernel density estimate is an efficient analysis method on the spatial layout. It could reveal the characters of layout form of shopping center on subway in essence. And it can also be applied to the other research of space form.

Keywords: Shanghai, shopping center on the subway, layout form, Kernel density estimate

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Authors: Gredson Keif Souza, Nehemias Curvelo Pereira

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Kernel oil from Macaúba is an important source of essential fatty acids. Thus, a new knowledge of the oil of this species could be used in new applications, such as pharmaceutical drugs based in the manufacture of cosmetics, and in various industrial processes. The aim of this study was to characterize the kernel oil of macaúba (Acrocomia Totai) at different times of their maturation. The physico-chemical characteristics were determined in accordance with the official analytical methods of oils and fats. It was determined the content of water and lipids in kernel, saponification value, acid value, water content in the oil, viscosity, density, composition in fatty acids by gas chromatography and molar mass. The results submitted to Tukey test for significant value to 5%. Found for the unripe fruits values superior to unsaturated fatty acids.

Keywords: extraction, characterization, kernel oil, acrocomia totai

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Authors: Faisal Zaman, Ya Ping Wong, Boon Yian Ng

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Point cloud source data for surface reconstruction is usually contaminated with noise and outliers. To overcome this, we present a novel approach using modified kernel density estimation (KDE) technique with bilateral filtering to remove noisy points and outliers. First we present a method for estimating optimal bandwidth of multivariate KDE using particle swarm optimization technique which ensures the robust performance of density estimation. Then we use mean-shift algorithm to find the local maxima of the density estimation which gives the centroid of the clusters. Then we compute the distance of a certain point from the centroid. Points belong to outliers then removed by automatic thresholding scheme which yields an accurate and economical point surface. The experimental results show that our approach comparably robust and efficient.

Keywords: point preprocessing, outlier removal, surface reconstruction, kernel density estimation

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Authors: Kiamran Radjabli

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State Estimator became an intrinsic part of Energy Management Systems (EMS). The SCADA measurements received from the field are processed by the State Estimator in order to accurately determine the actual operating state of the power systems and provide that information to other real-time network applications. All EMS vendors offer a State Estimator functionality in their baseline products. However, setting up and ensuring that State Estimator consistently produces a reliable solution often consumes a substantial engineering effort. This paper provides generic recommendations and describes a simple practical approach to efficient tuning of State Estimator, based on the working experience with major EMS software platforms and consulting projects in many electrical utilities of the USA.

Keywords: convergence, monitoring, state estimator, performance, troubleshooting, tuning, power systems

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Authors: Nelson Bii, Christopher Ouma, John Odhiambo

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Non-response is a potential source of errors in sample surveys. It introduces bias and large variance in the estimation of finite population parameters. Regression models have been recognized as one of the techniques of reducing bias and variance due to random non-response using auxiliary data. In this study, it is assumed that random non-response occurs in the survey variable in the second stage of cluster sampling, assuming full auxiliary information is available throughout. Auxiliary information is used at the estimation stage via a regression model to address the problem of random non-response. In particular, the auxiliary information is used via an improved Nadaraya-Watson kernel regression technique to compensate for random non-response. The asymptotic bias and mean squared error of the estimator proposed are derived. Besides, a simulation study conducted indicates that the proposed estimator has smaller values of the bias and smaller mean squared error values compared to existing estimators of finite population mean. The proposed estimator is also shown to have tighter confidence interval lengths at a 95% coverage rate. The results obtained in this study are useful, for instance, in choosing efficient estimators of the finite population mean in demographic sample surveys.

Keywords: mean squared error, random non-response, two-stage cluster sampling, confidence interval lengths

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Authors: D. Sigirli

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The Receiver Operating Characteristic (ROC) curve is a commonly used statistical tool for evaluating the diagnostic performance of screening and diagnostic test with continuous or ordinal scale results which aims to predict the presence or absence probability of a condition, usually a disease. When the test results were measured as numeric values, sensitivity and specificity can be computed across all possible threshold values which discriminate the subjects as diseased and non-diseased. There are infinite numbers of possible decision thresholds along the continuum of the test results. The ROC curve presents the trade-off between sensitivity and the 1-specificity as the threshold changes. The empirical ROC curve which is a non-parametric estimator of the ROC curve is robust and it represents data accurately. However, especially for small sample sizes, it has a problem of variability and as it is a step function there can be different false positive rates for a true positive rate value and vice versa. Besides, the estimated ROC curve being in a jagged form, since the true ROC curve is a smooth curve, it underestimates the true ROC curve. Since the true ROC curve is assumed to be smooth, several smoothing methods have been explored to smooth a ROC curve. These include using kernel estimates, using log-concave densities, to fit parameters for the specified density function to the data with the maximum-likelihood fitting of univariate distributions or to create a probability distribution by fitting the specified distribution to the data nd using smooth versions of the empirical distribution functions. In the present paper, we aimed to propose a smooth ROC curve estimation based on the boundary corrected kernel function and to compare the performances of ROC curve smoothing methods for the diagnostic test results coming from different distributions in different sample sizes. We performed simulation study to compare the performances of different methods for different scenarios with 1000 repetitions. It is seen that the performance of the proposed method was typically better than that of the empirical ROC curve and only slightly worse compared to the binormal model when in fact the underlying samples were generated from the normal distribution.

Keywords: empirical estimator, kernel function, smoothing, receiver operating characteristic curve

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Authors: Hamza Nejib, Okba Taouali

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This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS

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Authors: Alper Taner, Yesim Benal Oztekin, Huseyin Duran

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In this study, an Artificial Neural Network (ANN) was developed in order to classify barley varieties. For this purpose, physical properties of barley varieties were determined and ANN techniques were used. The physical properties of 8 barley varieties grown in Turkey, namely thousand kernel weight, geometric mean diameter, sphericity, kernel volume, surface area, bulk density, true density, porosity and colour parameters of grain, were determined and it was found that these properties were statistically significant with respect to varieties. As ANN model, three models, N-l, N-2 and N-3 were constructed. The performances of these models were compared. It was determined that the best-fit model was N-1. In the N-1 model, the structure of the model was designed to be 11 input layers, 2 hidden layers and 1 output layer. Thousand kernel weight, geometric mean diameter, sphericity, kernel volume, surface area, bulk density, true density, porosity and colour parameters of grain were used as input parameter; and varieties as output parameter. R2, Root Mean Square Error and Mean Error for the N-l model were found as 99.99%, 0.00074 and 0.009%, respectively. All results obtained by the N-l model were observed to have been quite consistent with real data. By this model, it would be possible to construct automation systems for classification and cleaning in flourmills.

Keywords: physical properties, artificial neural networks, barley, classification

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Authors: H. Ben Salah, A. Gannoun, C. de Peretti, A. Trabelsi

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The Downside Risk (DSR) model for portfolio optimisation allows to overcome the drawbacks of the classical mean-variance model concerning the asymetry of returns and the risk perception of investors. This model optimization deals with a positive definite matrix that is endogenous with respect to portfolio weights. This aspect makes the problem far more difficult to handle. For this purpose, Athayde (2001) developped a new recurcive minimization procedure that ensures the convergence to the solution. However, when a finite number of observations is available, the portfolio frontier presents an appearance which is not very smooth. In order to overcome that, Athayde (2003) proposed a mean kernel estimation of the returns, so as to create a smoother portfolio frontier. This technique provides an effect similar to the case in which we had continuous observations. In this paper, taking advantage on the the robustness of the median, we replace the mean estimator in Athayde's model by a nonparametric median estimator of the returns. Then, we give a new version of the former algorithm (of Athayde (2001, 2003)). We eventually analyse the properties of this improved portfolio frontier and apply this new method on real examples.

Keywords: Downside Risk, Kernel Method, Median, Nonparametric Estimation, Semivariance

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Authors: Zi Wang, Xinlei He, Jianghua Lv, Yuqing Lan

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Kernel though widely used, is complicated. Errors caused by some bugs are often costly. Statically, more than half of the mistakes occur in the design phase. Thus, we introduce a modeling method, KMVM (Linux Kernel Modeling and verification Method), based on type theory for proper designation and correct exploitation of the Kernel. In the model, the Kernel is separated into six levels: subsystem, dentry, file, struct, func, and base. Each level is treated as a type. The types are specified in the structure and relationship. At the same time, we use a demanding path to express the function to be implemented. The correctness of the design is verified by recursively checking the type relationship and type existence. The method has been applied to verify the OPEN business of VFS (virtual file system) in Linux Kernel. Also, we have designed and developed a set of security communication mechanisms in the Kernel with verification.

Keywords: formal approach, type theory, Linux Kernel, software program

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Authors: Diego Tancara, Raul Coto, Ariel Norambuena, Hoseein T. Dinani, Felipe Fanchini

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Quantum machine learning is a growing research field that aims to perform machine learning tasks assisted by a quantum computer. Kernel-based quantum machine learning models are paradigmatic examples where the kernel involves quantum states, and the Gram matrix is calculated from the overlapping between these states. With the kernel at hand, a regular machine learning model is used for the learning process. In this paper we investigate the quantum support vector machine and quantum kernel ridge models to predict the degree of non-Markovianity of a quantum system. We perform digital quantum simulation of amplitude damping and phase damping channels to create our quantum dataset. We elaborate on different kernel functions to map the data and kernel circuits to compute the overlapping between quantum states. We observe a good performance of the models.

Keywords: quantum, machine learning, kernel, non-markovianity

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Authors: Muhammad Jabbar

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In this paper we propose two ratio and ratio type exponential estimator for the estimation of population coefficient of variation using the auxiliary information under two-stage sampling. The properties of these estimators are derived up to first order of approximation. The efficiency conditions under which suggested estimator are more efficient, are obtained. Numerical and simulated studies are conducted to support the superiority of the estimators. Theoretically and numerically, we have found that our proposed estimator is always more efficient as compared to its competitor estimator.

Keywords: two-stage sampling, coefficient of variation, ratio type exponential estimator

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Authors: Jane A. Luke

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Persistent pressure passed on to manufacturers from escalating consumer expectations and the ever growing global competitiveness have produced a rapidly increasing interest in the development of various manufacturing strategy models. Academic and industrial circles are taking keen interest in the field of manufacturing strategy. Many manufacturing strategies are currently centered on the traditional concepts of focused manufacturing capabilities such as quality, cost, dependability and innovation. Process capability indices was conducted assuming that the process under study is in statistical control and independent observations are generated over time. However, in practice, it is very common to come across processes which, due to their inherent natures, generate autocorrelated observations. The degree of autocorrelation affects the behavior of patterns on control charts. Even, small levels of autocorrelation between successive observations can have considerable effects on the statistical properties of conventional control charts. When observations are autocorrelated the classical control charts exhibit nonrandom patterns and lack of control. Many authors have considered the effect of autocorrelation on the performance of statistical process control charts. In this paper, the effect of autocorrelation on confidence intervals for different PCIs was included. Stationary Gaussian processes is explained. Effect of autocorrelation on PCIs is described in detail. Confidence intervals for Cp and Cpk are constructed for PCIs when data are both independent and autocorrelated. Confidence intervals for Cp and Cpk are computed. Approximate lower confidence limits for various Cpk are computed assuming AR(1) model for the data. Simulation studies and industrial examples are considered to demonstrate the results.

Keywords: autocorrelation, AR(1) model, Bissell’s approximation, confidence intervals, statistical process control, specification limits, stationary Gaussian processes

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Authors: A. M. Abd-Elfattah, M. H. Abu-Moussa

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In this paper, the estimation of stress-strength parameter R = P(Y < X) is considered when X; Y the strength and stress respectively are two independent random variables of Burr Type XII distribution. The samples taken for X and Y are progressively censoring of type II. The maximum likelihood estimator (MLE) of R is obtained when the common parameter is unknown. But when the common parameter is known the MLE, uniformly minimum variance unbiased estimator (UMVUE) and the Bayes estimator of R = P(Y < X) are obtained. The exact condence interval of R based on MLE is obtained. The performance of the proposed estimators is compared using the computer simulation.

Keywords: Burr Type XII distribution, progressive type-II censoring, stress-strength model, unbiased estimator, maximum-likelihood estimator, uniformly minimum variance unbiased estimator, confidence intervals, Bayes estimator

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Authors: Habshah Midi, Mohammed A. Mohammed, Sohel Rana

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Multicollinearity occurs when two or more independent variables in a multiple linear regression model are highly correlated. The ridge regression is the commonly used method to rectify this problem. However, the ridge regression cannot handle the problem of multicollinearity which is caused by high leverage collinearity enhancing observation (HLCEO). Since high leverage points (HLPs) are responsible for inducing multicollinearity, the effect of HLPs needs to be reduced by using Generalized M estimator. The existing GM6 estimator is based on the Minimum Volume Ellipsoid (MVE) which tends to swamp some low leverage points. Hence an improvised GM (MGM) estimator is presented to improve the precision of the GM6 estimator. Numerical example and simulation study are presented to show how HLPs can cause multicollinearity. The numerical results show that our MGM estimator is the most efficient method compared to some existing methods.

Keywords: identification, high leverage points, multicollinearity, GM-estimator, DRGP, DFFITS

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Authors: Kazi Md. Shifun Newaz, S. Miaji, Shahnewaz Hazanat-E-Rabbi

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In this study, the kernel density estimation tool has been used to identify most crash prone locations in a national highway of Bangladesh. Like other developing countries, in Bangladesh road traffic crashes (RTC) have now become a great social alarm and the situation is deteriorating day by day. Today’s black spot identification process is not based on modern technical tools and most of the cases provide wrong output. In this situation, characteristic analysis and black spot identification by spatial analysis would be an effective and low cost approach in ensuring road safety. The methodology of this study incorporates a framework on the basis of spatial-temporal study to identify most RTC occurrence locations. In this study, a very important and economic corridor like Dhaka to Sylhet highway has been chosen to apply the method. This research proposes that KDE method for identification of Hazardous Road Location (HRL) could be used for all other National highways in Bangladesh and also for other developing countries. Some recommendations have been suggested for policy maker to reduce RTC in Dhaka-Sylhet especially in black spots.

Keywords: hazardous road location (HRL), crash, GIS, kernel density

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Authors: Hasik Lee, Seung-Young Kho

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Nowadays, automatic fare collection (AFC) system is widely used in many countries. However, smart card data from many of cities does not contain alighting information which is necessary to build OD matrices. Therefore, in order to utilize smart card data, destinations of passengers should be estimated. In this paper, kernel density estimation was used to forecast probabilities of alighting stations of bus passengers and applied to smart card data in Seoul, Korea which contains boarding and alighting information. This method was also validated with actual data. In some cases, stochastic method was more accurate than deterministic method. Therefore, it is sufficiently accurate to be used to build OD matrices.

Keywords: destination estimation, Kernel density estimation, smart card data, validation

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Authors: Arum Kingsley Chinedu, Ugwuowo Fidelis Ifeanyi, Oranye Henrietta Ebele

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The Poisson regression model (PRM) is a nonlinear model that belongs to the exponential family of distribution. PRM is suitable for studying count variables using appropriate covariates and sometimes experiences the problem of multicollinearity in the explanatory variables and outliers on the response variable. This study aims to address the problem of multicollinearity and outliers jointly in a Poisson regression model. We developed an estimator called the robust modified jackknife PCKL parameter estimator by combining the principal component estimator, modified jackknife KL and transformed M-estimator estimator to address both problems in a PRM. The superiority conditions for this estimator were established, and the properties of the estimator were also derived. The estimator inherits the characteristics of the combined estimators, thereby making it efficient in addressing both problems. And will also be of immediate interest to the research community and advance this study in terms of novelty compared to other studies undertaken in this area. The performance of the estimator (robust modified jackknife PCKL) with other existing estimators was compared using mean squared error (MSE) as a performance evaluation criterion through a Monte Carlo simulation study and the use of real-life data. The results of the analytical study show that the estimator outperformed other existing estimators compared with by having the smallest MSE across all sample sizes, different levels of correlation, percentages of outliers and different numbers of explanatory variables.

Keywords: jackknife modified KL, outliers, multicollinearity, principal component, transformed M-estimator.

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Authors: Serge Provost, Yishan Zang

Abstract:

Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.

Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation

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Authors: Ya-Mei Chang

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This research is intended to apply spatio-temporal point process methods to the dengue fever data in Tainan. The spatio-temporal intensity function of the dataset is assumed to be separable. The kernel estimation is a widely used approach to estimate intensity functions. The intensity function is very helpful to study the relation of the spatio-temporal point process and some covariates. The covariate effects might be nonlinear. An nonparametric smoothing estimator is used to detect the nonlinearity of the covariate effects. A fitted parametric model could describe the influence of the covariates to the dengue fever. The correlation between the data points is detected by the K-function. The result of this research could provide useful information to help the government or the stakeholders making decisions.

Keywords: dengue fever, spatial point process, kernel estimation, covariate effect

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Authors: E. D. Paul, A. D. Adams, O. Sunmonu, U. S. Ishiaku

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Activated tamarind kernel powder (ATKP) was prepared from tamarind fruit (Tamarindus indica), and utilized for the removal of Reactive Blue 29 (RB29) from its aqueous solution. The powder was activated using 4N nitric acid (HNO₃). The adsorbent was characterised using infrared spectroscopy, bulk density, ash content, pH, moisture content and dry matter content measurements. The effect of various parameters which include; temperature, pH, adsorbent dosage, ion concentration, and contact time were studied. Four different equilibrium isotherm models were tested on the experimental data, but the Temkin isotherm model was best-fitted into the experimental data. The pseudo-first order and pseudo-second-order kinetic models were also fitted into the graphs, but pseudo-second order was best fitted to the experimental data. The thermodynamic parameters showed that the adsorption of Reactive Blue 29 onto activated tamarind kernel powder is a physical process, feasible and spontaneous, exothermic in nature and there is decreased randomness at the solid/solution interphase during the adsorption process. Therefore, activated tamarind kernel powder has proven to be a very good adsorbent for the removal of Reactive Blue 29 dyes from industrial waste water.

Keywords: tamarind kernel powder, reactive blue 29, isotherms, kinetics

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Authors: Marzieh Ahmadi, Ruhullah Alikhan Gorgani

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The usual methods of measuring regional inequalities can not reflect the internal changes of the country in terms of their displacement in different development groups, and the indicators of inequalities are not effective in demonstrating the dynamics of the distribution of inequality. For this purpose, this paper examines the dynamics of the urban inertial transport in the country during the period of 2006-2016 using the CIRD multidimensional index and stochastic kernel density method. it firstly selects 25 indicators in five dimensions including macroeconomic conditions, science and innovation, environmental sustainability, human capital and public facilities, and two-stage Principal Component Analysis methodology are developed to create a composite index of inequality. Then, in the second stage, using a nonparametric analytical approach to internal distribution dynamics and a stochastic kernel density method, the convergence hypothesis of the CIRD index of the Iranian provinces center is tested, and then, based on the ergodic density, long-run equilibrium is shown. Also, at this stage, for the purpose of adopting accurate regional policies, the distribution dynamics and process of convergence or divergence of the Iranian provinces for each of the five. According to the results of the first Stage, in 2006 & 2016, the highest level of development is related to Tehran and zahedan is at the lowest level of development. The results show that the central cities of the country are at the highest level of development due to the effects of Tehran's knowledge spillover and the country's lower cities are at the lowest level of development. The main reason for this may be the lack of access to markets in the border provinces. Based on the results of the second stage, which examines the dynamics of regional inequality transmission in the country during 2006-2016, the first year (2006) is not multifaceted and according to the kernel density graph, the CIRD index of about 70% of the cities. The value is between -1.1 and -0.1. The rest of the sequence on the right is distributed at a level higher than -0.1. In the kernel distribution, a convergence process is observed and the graph points to a single peak. Tends to be a small peak at about 3 but the main peak at about-0.6. According to the chart in the final year (2016), the multidimensional pattern remains and there is no mobility in the lower level groups, but at the higher level, the CIRD index accounts for about 45% of the provinces at about -0.4 Take it. That this year clearly faces the twin density pattern, which indicates that the cities tend to be closely related to each other in terms of development, so that the cities are low in terms of development. Also, according to the distribution dynamics results, the provinces of Iran follow the single-density density pattern in 2006 and the double-peak density pattern in 2016 at low and moderate inequality index levels and also in the development index. The country diverges during the years 2006 to 2016.

Keywords: Urban Disparity, CIRD Index, Convergence, Distribution Dynamics, Random Kernel Density

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Authors: Serge B. Provost

Abstract:

Numerous statistical inference and modeling methodologies are based on sample moments rather than the actual observations. A result justifying the validity of this approach is introduced. More specifically, it will be established that given the first n moments of a sample of size n, one can recover the original n sample points. This implies that a sample of size n and its first associated n moments contain precisely the same amount of information. However, it is efficient to make use of a limited number of initial moments as most of the relevant distributional information is included in them. Two types of density estimation techniques that rely on such moments will be discussed. The first one expresses a density estimate as the product of a suitable base density and a polynomial adjustment whose coefficients are determined by equating the moments of the density estimate to the sample moments. The second one assumes that the derivative of the logarithm of a density function can be represented as a rational function. This gives rise to a system of linear equations involving sample moments, the density estimate is then obtained by solving a differential equation. Unlike kernel density estimation, these methodologies are ideally suited to model ‘big data’ as they only require a limited number of moments, irrespective of the sample size. What is more, they produce simple closed form expressions that are amenable to algebraic manipulations. They also turn out to be more accurate as will be shown in several illustrative examples.

Keywords: density estimation, log-density, polynomial adjustments, sample moments

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