Search results for: estimators

Authors: Muhammad Nouman Qureshi, Muhammad Hanif

Abstract:

Adaptive cluster sampling (ACS) is specifically developed for the estimation of highly clumped populations and applied to a wide range of situations like animals of rare and endangered species, uneven minerals, HIV patients and drug users. In this paper, we proposed a generalized semi-exponential estimator with two auxiliary variables under the framework of ACS design. The expressions of approximate bias and mean square error (MSE) of the proposed estimator are derived. Theoretical comparisons of the proposed estimator have been made with existing estimators. A numerical study is conducted on real and artificial populations to demonstrate and compare the efficiencies of the proposed estimator. The results indicate that the proposed generalized semi-exponential estimator performed considerably better than all the adaptive and non-adaptive estimators considered in this paper.

Keywords: auxiliary information, adaptive cluster sampling, clustered populations, Hansen-Hurwitz estimation

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Authors: B. Siva Kumar Reddy, B. Lakshmi

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WiMAX has adopted an Adaptive Modulation and Coding (AMC) in OFDM to endure higher data rates and error free transmission. AMC schemes employ the Channel State Information (CSI) to efficiently utilize the channel and maximize the throughput and for better spectral efficiency. This CSI has given to the transmitter by the channel estimators. In this paper, LSE (Least Square Error) and MMSE (Minimum Mean square Error) estimators are suggested and BER (Bit Error Rate) performance has been analyzed. Channel equalization is also integrated with with AMC-OFDM system and presented with Constant Modulus Algorithm (CMA) and Least Mean Square (LMS) algorithms with convergence rates analysis. Simulation results proved that increment in modulation scheme size causes to improvement in throughput along with BER value. There is a trade-off among modulation size, throughput, BER value and spectral efficiency. Results also reported the requirement of channel estimation and equalization in high data rate systems.

Keywords: AMC, CSI, CMA, OFDM, OFDMA, WiMAX

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Authors: Alan Wan

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In recent years, the body of literature on frequentist model averaging in statistics has grown significantly. Most of this work focuses on models with different mean structures but leaves out the variance consideration. In this paper, we consider a regression model with multiplicative heteroscedasticity and develop a model averaging method that combines maximum likelihood estimators of unknown parameters in both the mean and variance functions of the model. Our weight choice criterion is based on a minimisation of a plug-in estimator of the model average estimator's squared prediction risk. We prove that the new estimator possesses an asymptotic optimality property. Our investigation of finite-sample performance by simulations demonstrates that the new estimator frequently exhibits very favourable properties compared to some existing heteroscedasticity-robust model average estimators. The model averaging method hedges against the selection of very bad models and serves as a remedy to variance function misspecification, which often discourages practitioners from modeling heteroscedasticity altogether. The proposed model average estimator is applied to the analysis of two real data sets.

Keywords: heteroscedasticity-robust, model averaging, multiplicative heteroscedasticity, plug-in, squared prediction risk

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Authors: Shahadut Hossain, Jacek Wesolowski, Zahirul Hoque

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In many epidemiological and environmental studies covariate measurements are subject to the detection limit. In most applications, covariate measurements are usually truncated from below which is known as left-truncation. Because the measuring device, which we use to measure the covariate, fails to detect values falling below the certain threshold. In regression analyses, it causes inflated bias and inaccurate mean squared error (MSE) to the estimators. This paper suggests a response-based regression calibration method to correct the deleterious impact introduced by the covariate detection limit in the estimators of the parameters of simple logistic regression model. Compared to the maximum likelihood method, the proposed method is computationally simpler, and hence easier to implement. It is robust to the violation of distributional assumption about the covariate of interest. In producing correct inference, the performance of the proposed method compared to the other competing methods has been investigated through extensive simulations. A real-life application of the method is also shown using data from a population-based case-control study of non-Hodgkin lymphoma.

Keywords: environmental exposure, detection limit, left truncation, bias, ad-hoc substitution

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Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

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Authors: Fu Jinyu, Lin Jinguan

Abstract:

This paper introduces a novel approach that unifies two types of models: one is the continuous-time jump-diffusion used to model high-frequency data, and the other is discrete-time GQARCH employed to model low-frequency financial data by embedding the discrete GQARCH structure with jumps in the instantaneous volatility process. This model is named “GQARCH-It\^{o} -Jumps mode.” We adopt the realized range-based threshold estimation for high-frequency financial data rather than the realized return-based volatility estimators, which entail the loss of intra-day information of the price movement. Meanwhile, a quasi-likelihood function for the low-frequency GQARCH structure with jumps is developed for the parametric estimate. The asymptotic theories are mainly established for the proposed estimators in the case of finite activity jumps. Moreover, simulation studies are implemented to check the finite sample performance of the proposed methodology. Specifically, it is demonstrated that how our proposed approaches can be practically used on some financial data.

Keywords: It\^{o} process, GQARCH, leverage effects, threshold, realized range-based volatility estimator, quasi-maximum likelihood estimate

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Authors: Fatemah A. Alqallaf, Debasis Kundu

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The aim of this paper is to introduce a bivariate inverse generalized exponential distribution which has a singular component. The proposed bivariate distribution can be used when the marginals have heavy-tailed distributions, and they have non-monotone hazard functions. Due to the presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution, and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four-dimensional optimization problem. To avoid that, we have proposed to use an EM algorithm, and it involves solving only one non-linear equation at each `E'-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the proposed bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the proposed model.

Keywords: Block and Basu bivariate distributions, competing risks, EM algorithm, Marshall-Olkin bivariate exponential distribution, maximum likelihood estimators

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Authors: Juan F. Muñoz-Rosas, Rosa M. García-Fernández, Encarnación Álvarez-Verdejo, Pablo J. Moya-Fernández

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Poverty measurement is a very important topic in many studies in social sciences. One of the most important indicators when measuring poverty is the low income proportion. This indicator gives the proportion of people of a population classified as poor. This indicator is generally unknown, and for this reason, it is estimated by using survey data, which are obtained by official surveys carried out by many statistical agencies such as Eurostat. The main feature of the mentioned survey data is the fact that they contain several variables. The variable used to estimate the low income proportion is called as the variable of interest. The survey data may contain several additional variables, also named as the auxiliary variables, related to the variable of interest, and if this is the situation, they could be used to improve the estimation of the low income proportion. In this paper, we use Monte Carlo simulation studies to analyze numerically the performance of estimators based on several auxiliary variables. In this simulation study, we considered real data sets obtained from the 2011 European Union Survey on Income and Living Condition. Results derived from this study indicate that the estimators based on auxiliary variables are more accurate than the naive estimator.

Keywords: inclusion probability, poverty, poverty line, survey sampling

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Authors: M. Z. Raqab, Debasis Kundu, M. A. Meraou

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In this paper, we have analyzed maximum precipitation data during a particular period of time obtained from different stations in the Global Historical Climatological Network of the USA. One important point to mention is that some stations are shut down on certain days for some reason or the other. Hence, the maximum values are recorded by excluding those readings. It is assumed that the number of stations that operate follows zero-truncated Poisson random variables, and the daily precipitation follows a lognormal random variable. We call this model a compound truncated Poisson lognormal model. The proposed model has three unknown parameters, and it can take a variety of shapes. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals also can be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model, it is observed that the proposed model provides a better fit than some of the existing models.

Keywords: compound Poisson lognormal distribution, EM algorithm, maximum likelihood estimation, approximate maximum likelihood estimation, Fisher information, skew distribution

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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: Bastien Batardière, Joon Kwon

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For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past gradients and thereby adapt to the geometry of the objective function. Variants such as RMSprop and Adam demonstrate outstanding practical performance that have contributed to the success of deep learning. In this work, we present AdaLVR, which combines the AdaGrad algorithm with loopless variance-reduced gradient estimators such as SAGA or L-SVRG that benefits from a straightforward construction and a streamlined analysis. We assess that AdaLVR inherits both good convergence properties from VR methods and the adaptive nature of AdaGrad: in the case of L-smooth convex functions we establish a gradient complexity of O(n + (L + √ nL)/ε) without prior knowledge of L. Numerical experiments demonstrate the superiority of AdaLVR over state-of-the-art methods. Moreover, we empirically show that the RMSprop and Adam algorithm combined with variance-reduced gradients estimators achieve even faster convergence.

Keywords: convex optimization, variance reduction, adaptive algorithms, loopless

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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: Yemane Hailu Fissuh, Zhongzhan Zhang

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An estimating equation technique is an alternative method of the widely used maximum likelihood methods, which enables us to ease some complexity due to the complex characteristics of time-varying covariates. In the situations, when both the time-varying covariates and left-truncation are considered in the model, the maximum likelihood estimation procedures become much more burdensome and complex. To ease the complexity, in this study, the modified estimating equations those have been given high attention and considerations in many researchers under semiparametric transformation model was proposed. The purpose of this article was to develop the modified estimating equation under flexible and general class of semiparametric transformation models for left-truncated and right censored survival data with time-varying covariates. Besides the commonly applied Cox proportional hazards model, such kind of problems can be also analyzed with a general class of semiparametric transformation models to estimate the effect of treatment given possibly time-varying covariates on the survival time. The consistency and asymptotic properties of the estimators were intuitively derived via the expectation-maximization (EM) algorithm. The characteristics of the estimators in the finite sample performance for the proposed model were illustrated via simulation studies and Stanford heart transplant real data examples. To sum up the study, the bias for covariates has been adjusted by estimating density function for the truncation time variable. Then the effect of possibly time-varying covariates was evaluated in some special semiparametric transformation models.

Keywords: EM algorithm, estimating equation, semiparametric transformation models, time-to-event outcomes, time varying covariate

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Authors: Karima Kimouche

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In this paper, we consider the asymptotic problems in spectral analysis of stationary causal random fields. We impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear random fields. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given.

Keywords: spatial nonlinear processes, spectral estimators, GMC condition, bootstrap method

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Authors: Jackson Niyongabo

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This study addresses a notable gap in the existing literature on the relationship between energy consumption, economic growth, and CO₂ emissions, particularly within the African context. While numerous studies have explored these dynamics globally and regionally across various development levels, few have delved into the nuances of regions and income levels specific to African countries. Furthermore, the evaluation of the interplay between green growth policies, green energy technologies, and their impact on environmental quality has been underexplored. This research aims to fill these gaps by conducting a comprehensive analysis of the transition from conventional economic growth and energy consumption to a paradigm of green growth coupled with green energy utilization across the African continent from 1980 to 2018. The study is structured into three main parts: an empirical examination of the long-term effects of energy intensity, renewable energy consumption, and economic growth on CO₂ emissions across diverse African regions and income levels; an estimation of the long-term impact of green growth and green energy use on CO₂ emissions for countries implementing green policies within Africa, as well as at regional and global levels; and a comparative analysis of the impact of green growth policies on environmental degradation before and after implementation. Employing advanced econometric methods and panel estimators, the study utilizes a testing framework, panel unit tests, and various estimators to derive meaningful insights. The anticipated results and conclusions will be elucidated through causality tests, impulse response, and variance decomposition analyses, contributing valuable knowledge to the discourse on sustainable development in the African context.

Keywords: economic growth, green growth, energy consumption, CO₂ emissions, econometric models, green energy

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Authors: Yan Torres, Fernanda Simoes, Francisco Petrucci-Fonseca, Freddie-Jeanne Richard

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The non-invasive samples are an alternative of collecting genetic samples directly. Non-invasive samples are collected without the manipulation of the animal (e.g., scats, feathers and hairs). Nevertheless, the use of non-invasive samples has some limitations. The main issue is degraded DNA, leading to poorer extraction efficiency and genotyping. Those errors delayed for some years a widespread use of non-invasive genetic information. Possibilities to limit genotyping errors can be done using analysis methods that can assimilate the errors and singularities of non-invasive samples. Genotype matching and population estimation algorithms can be highlighted as important analysis tools that have been adapted to deal with those errors. Although, this recent development of analysis methods there is still a lack of empirical performance comparison of them. A comparison of methods with dataset different in size and structure can be useful for future studies since non-invasive samples are a powerful tool for getting information specially for endangered and rare populations. To compare the analysis methods, four different datasets used were obtained from the Dryad digital repository were used. Three different matching algorithms (Cervus, Colony and Error Tolerant Likelihood Matching - ETLM) are used for matching genotypes and two different ones for population estimation (Capwire and BayesN). The three matching algorithms showed different patterns of results. The ETLM produced less number of unique individuals and recaptures. A similarity in the matched genotypes between Colony and Cervus was observed. That is not a surprise since the similarity between those methods on the likelihood pairwise and clustering algorithms. The matching of ETLM showed almost no similarity with the genotypes that were matched with the other methods. The different cluster algorithm system and error model of ETLM seems to lead to a more criterious selection, although the processing time and interface friendly of ETLM were the worst between the compared methods. The population estimators performed differently regarding the datasets. There was a consensus between the different estimators only for the one dataset. The BayesN showed higher and lower estimations when compared with Capwire. The BayesN does not consider the total number of recaptures like Capwire only the recapture events. So, this makes the estimator sensitive to data heterogeneity. Heterogeneity in the sense means different capture rates between individuals. In those examples, the tolerance for homogeneity seems to be crucial for BayesN work properly. Both methods are user-friendly and have reasonable processing time. An amplified analysis with simulated genotype data can clarify the sensibility of the algorithms. The present comparison of the matching methods indicates that Colony seems to be more appropriated for general use considering a time/interface/robustness balance. The heterogeneity of the recaptures affected strongly the BayesN estimations, leading to over and underestimations population numbers. Capwire is then advisable to general use since it performs better in a wide range of situations.

Keywords: algorithms, genetics, matching, population

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Authors: Rafid Saeed Abdulrazak Alshkaki

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In this paper, zero-one inflated negative binomial distribution is considered, along with some of its structural properties, then its parameters were estimated using the method of moments. It is found that the method of moments to estimate the parameters of the zero-one inflated negative binomial models is not a proper method and may give incorrect conclusions.

Keywords: zero one inflated models, negative binomial distribution, moments estimator, non negative integer sampling

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Authors: Brahim Boukabcha, Amar Rebbouh

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The bootstrap method based on the idea of exploiting all the information provided by the initial sample, allows us to study the properties of estimators. In this article we will present a theoretical study on the different methods of bootstrapping and using the technique of re-sampling in statistics inference to calculate the standard error of means of an estimator and determining a confidence interval for an estimated parameter. We apply these methods tested in the regression models and Pareto model, giving the best approximations.

Keywords: bootstrap, error standard, bias, jackknife, mean, median, variance, confidence interval, regression models

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Authors: Abdullah Eqal Al Mazrooei

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In this paper, we introduce a mathematical algorithm which is used for estimating the states in the bilinear systems. This algorithm uses a special linearization of the second-order term by using the best available information about the state of the system. This technique makes our algorithm generalizes the well-known Kalman estimators. The system which is used here is of the bilinear class, the evolution of this model is linear-bilinear in the state of the system. Our algorithm can be used with linear and bilinear systems. We also here introduced a real application for the new algorithm to prove the feasibility and the efficiency for it.

Keywords: estimation algorithm, bilinear systems, Kakman filter, second order linearization

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Authors: Zhou Jianhong

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Model averaging is a desirable approach to deal with model uncertainty, which, however, has rarely been explored for Poisson regression. In this paper, we propose a model averaging procedure based on an unbiased estimator of the expected Kullback-Leibler distance for the Poisson regression. Simulation study shows that the proposed model average estimator outperforms some other commonly used model selection and model average estimators in some situations. Our proposed methods are further applied to a real data example and the advantage of this method is demonstrated again.

Keywords: model averaging, poission regression, Kullback-Leibler distance, statistics

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Authors: Yemane Hailu Fissuh, Zhongzhan Zhang

Abstract:

In biomedical researches and randomized clinical trials, the most commonly interested outcomes are time-to-event so-called survival data. The importance of robust models in this context is to compare the effect of randomly controlled experimental groups that have a sense of causality. Causal estimation is the scientific concept of comparing the pragmatic effect of treatments conditional to the given covariates rather than assessing the simple association of response and predictors. Hence, the causal effect based semiparametric transformation model was proposed to estimate the effect of treatment with the presence of possibly time-varying covariates. Due to its high flexibility and robustness, the semiparametric transformation model which shall be applied in this paper has been given much more attention for estimation of a causal effect in modeling left-truncated and right censored survival data. Despite its wide applications and popularity in estimating unknown parameters, the maximum likelihood estimation technique is quite complex and burdensome in estimating unknown parameters and unspecified transformation function in the presence of possibly time-varying covariates. Thus, to ease the complexity we proposed the modified estimating equations. After intuitive estimation procedures, the consistency and asymptotic properties of the estimators were derived and the characteristics of the estimators in the finite sample performance of the proposed model were illustrated via simulation studies and Stanford heart transplant real data example. To sum up the study, the bias of covariates was adjusted via estimating the density function for truncation variable which was also incorporated in the model as a covariate in order to relax the independence assumption of failure time and truncation time. Moreover, the expectation-maximization (EM) algorithm was described for the estimation of iterative unknown parameters and unspecified transformation function. In addition, the causal effect was derived by the ratio of the cumulative hazard function of active and passive experiments after adjusting for bias raised in the model due to the truncation variable.

Keywords: causal estimation, EM algorithm, semiparametric transformation models, time-to-event outcomes, time-varying covariate

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Authors: Juan M. Rodriguez-Diaz

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The precision of parameter estimators in the Gaussian linear model is traditionally accounted by the variance-covariance matrix of the asymptotic distribution. However, this measure can underestimate the true variance, specially for small samples. Traditionally, optimal design theory pays attention to this variance through its relationship with the model's information matrix. For this reason it seems convenient, at least in some cases, adapt the optimality criteria in order to get the best designs for the actual variance structure, otherwise the loss in efficiency of the designs obtained with the traditional approach may be very important.

Keywords: correlated observations, information matrix, optimality criteria, variance-covariance matrix

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Authors: Mahdy ‎Esmailian, Mahdi ‎Doostparast, Ahmad ‎Parsian

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‎In this article‎, ‎sequential order statistics (SOS) censoring type II samples coming from the generalized Pareto distribution are considered‎. ‎Maximum likelihood (ML) estimators of the unknown parameters are derived on the basis of the available multiple SOS data‎. ‎Necessary conditions for existence and uniqueness of the derived ML estimates are given‎. Due to complexity in the proposed likelihood function‎, ‎a useful re-parametrization is suggested‎. ‎For illustrative purposes‎, ‎a Monte Carlo simulation study is conducted and an illustrative example is analysed‎.

Keywords: bayesian estimation‎, generalized pareto distribution‎, ‎maximum likelihood estimation‎, sequential order statistics

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Authors: Brouri Adil, Giri Fouad

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The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: Yemane Hailu Fissuh, Zhongzhan Zhang

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a systematic observation from a defined time of origin up to certain failure or censor is known as survival data. Survival analysis is a major area of interest in biostatistics and biomedical researches. At the heart of understanding, the most scientific and medical research inquiries lie for a causality analysis. Thus, the main concern of this study is to investigate the causal effect of treatment on survival time conditional to the possibly time-varying covariates. The theory of causality often differs from the simple association between the response variable and predictors. A causal estimation is a scientific concept to compare a pragmatic effect between two or more experimental arms. To evaluate an average treatment effect on survival outcome, the estimating equation was adjusted for time-varying covariates under the semi-parametric transformation models. The proposed model intuitively obtained the consistent estimators for unknown parameters and unspecified monotone transformation functions. In this article, the proposed method estimated an unbiased average causal effect of treatment on survival time of interest. The modified estimating equations of semiparametric transformation models have the advantage to include the time-varying effect in the model. Finally, the finite sample performance characteristics of the estimators proved through the simulation and Stanford heart transplant real data. To this end, the average effect of a treatment on survival time estimated after adjusting for biases raised due to the high correlation of the left-truncation and possibly time-varying covariates. The bias in covariates was restored, by estimating density function for left-truncation. Besides, to relax the independence assumption between failure time and truncation time, the model incorporated the left-truncation variable as a covariate. Moreover, the expectation-maximization (EM) algorithm iteratively obtained unknown parameters and unspecified monotone transformation functions. To summarize idea, the ratio of cumulative hazards functions between the treated and untreated experimental group has a sense of the average causal effect for the entire population.

Keywords: a modified estimation equation, causal effect, semiparametric transformation models, survival analysis, time-varying covariate

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Authors: Fabiano Araujo Soares, Sauro Emerick Salomoni, Joao Paulo Lima da Silva, Igor Luiz Moura, Adson Ferreira da Rocha

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This paper presents a tool developed in the Matlab platform. It was developed to simplify the analysis of surface electromyography signals (S-EMG) in a way accessible to users that are not familiarized with signal processing procedures. The tool receives data by commands in window fields and generates results as graphics and excel tables. The underlying math of each S-EMG estimator is presented. Setup window and result graphics are presented. The tool was presented to four non-engineer users and all of them managed to appropriately use it after a 5 minutes instruction period.

Keywords: S-EMG estimators, electromyography, surface electromyography, ARV, RMS, MDF, MNF, CV

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Authors: Hazem M. Al-Mofleh

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In this paper, a new four-parameter univariate continuous distribution called the Normal-Generalized Hyperbolic Secant Distribution (NGHS) is defined and studied. Some general and structural distributional properties are investigated and discussed, including: central and non-central n-th moments and incomplete moments, quantile and generating functions, hazard function, Rényi and Shannon entropies, shapes: skewed right, skewed left, and symmetric, modality regions: unimodal and bimodal, maximum likelihood (MLE) estimators for the parameters. Finally, two real data sets are used to demonstrate empirically its flexibility and prove the strength of the new distribution.

Keywords: bimodality, estimation, hazard function, moments, Shannon’s entropy

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Authors: Tea Poklepović, Zdravka Aljinović, Mario Matković

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Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and compares three efficient frontiers on the Croatian Stock Market. The results show that range-based volatility estimator outperforms both mean-variance and lower semi-variance model.

Keywords: variance, lower semi-variance, range-based volatility, MPT

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Authors: Mahmoud I. Syam, Kamarulzaman Ibrahim, Amer I. Al-Omari

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Stratified double extreme ranked set sampling (SDERSS) method is introduced and considered for estimating the population mean. The SDERSS is compared with the simple random sampling (SRS), stratified ranked set sampling (SRSS) and stratified simple set sampling (SSRS). It is shown that the SDERSS estimator is an unbiased of the population mean and more efficient than the estimators using SRS, SRSS and SSRS when the underlying distribution of the variable of interest is symmetric or asymmetric.

Keywords: double extreme ranked set sampling, extreme ranked set sampling, ranked set sampling, stratified double extreme ranked set sampling

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Authors: Huseyin Guler, Cigdem Kosar

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The aim of this study is to propose Bridge estimator for seasonal unit root tests. Seasonality is an important factor for many economic time series. Some variables may contain seasonal patterns and forecasts that ignore important seasonal patterns have a high variance. Therefore, it is very important to eliminate seasonality for seasonal macroeconomic data. There are some methods to eliminate the impacts of seasonality in time series. One of them is filtering the data. However, this method leads to undesired consequences in unit root tests, especially if the data is generated by a stochastic seasonal process. Another method to eliminate seasonality is using seasonal dummy variables. Some seasonal patterns may result from stationary seasonal processes, which are modelled using seasonal dummies but if there is a varying and changing seasonal pattern over time, so the seasonal process is non-stationary, deterministic seasonal dummies are inadequate to capture the seasonal process. It is not suitable to use seasonal dummies for modeling such seasonally nonstationary series. Instead of that, it is necessary to take seasonal difference if there are seasonal unit roots in the series. Different alternative methods are proposed in the literature to test seasonal unit roots, such as Dickey, Hazsa, Fuller (DHF) and Hylleberg, Engle, Granger, Yoo (HEGY) tests. HEGY test can be also used to test the seasonal unit root in different frequencies (monthly, quarterly, and semiannual). Another issue in unit root tests is the lag selection. Lagged dependent variables are added to the model in seasonal unit root tests as in the unit root tests to overcome the autocorrelation problem. In this case, it is necessary to choose the lag length and determine any deterministic components (i.e., a constant and trend) first, and then use the proper model to test for seasonal unit roots. However, this two-step procedure might lead size distortions and lack of power in seasonal unit root tests. Recent studies show that Bridge estimators are good in selecting optimal lag length while differentiating nonstationary versus stationary models for nonseasonal data. The advantage of this estimator is the elimination of the two-step nature of conventional unit root tests and this leads a gain in size and power. In this paper, the Bridge estimator is proposed to test seasonal unit roots in a HEGY model. A Monte-Carlo experiment is done to determine the efficiency of this approach and compare the size and power of this method with HEGY test. Since Bridge estimator performs well in model selection, our approach may lead to some gain in terms of size and power over HEGY test.

Keywords: bridge estimators, HEGY test, model selection, seasonal unit root

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