Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3896

Search results for: maximum likelihood estimator (MLE)

3896 Survival and Hazard Maximum Likelihood Estimator with Covariate Based on Right Censored Data of Weibull Distribution

Authors: Al Omari Mohammed Ahmed

Abstract:

This paper focuses on Maximum Likelihood Estimator with Covariate. Covariates are incorporated into the Weibull model. Under this regression model with regards to maximum likelihood estimator, the parameters of the covariate, shape parameter, survival function and hazard rate of the Weibull regression distribution with right censored data are estimated. The mean square error (MSE) and absolute bias are used to compare the performance of Weibull regression distribution. For the simulation comparison, the study used various sample sizes and several specific values of the Weibull shape parameter.

Keywords: weibull regression distribution, maximum likelihood estimator, survival function, hazard rate, right censoring

Procedia PDF Downloads 353
3895 Estimation of Stress-Strength Parameter for Burr Type XII Distribution Based on Progressive Type-II Censoring

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

Abstract:

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

Procedia PDF Downloads 368
3894 An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods

Authors: Autcha Araveeporn

Abstract:

This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov chain Monte Carlo method, maximum likelihood method, normal distribution

Procedia PDF Downloads 278
3893 Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution

Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

Abstract:

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

Procedia PDF Downloads 271
3892 Parameters Estimation of Power Function Distribution Based on Selective Order Statistics

Authors: Moh'd Alodat

Abstract:

In this paper, we discuss the power function distribution and derive the maximum likelihood estimator of its parameter as well as the reliability parameter. We derive the large sample properties of the estimators based on the selective order statistic scheme. We conduct simulation studies to investigate the significance of the selective order statistic scheme in our setup and to compare the efficiency of the new proposed estimators.

Keywords: fisher information, maximum likelihood estimator, power function distribution, ranked set sampling, selective order statistics sampling

Procedia PDF Downloads 336
3891 A Kolmogorov-Smirnov Type Goodness-Of-Fit Test of Multinomial Logistic Regression Model in Case-Control Studies

Authors: Chen Li-Ching

Abstract:

The multinomial logistic regression model is used popularly for inferring the relationship of risk factors and disease with multiple categories. This study based on the discrepancy between the nonparametric maximum likelihood estimator and semiparametric maximum likelihood estimator of the cumulative distribution function to propose a Kolmogorov-Smirnov type test statistic to assess adequacy of the multinomial logistic regression model for case-control data. A bootstrap procedure is presented to calculate the critical value of the proposed test statistic. Empirical type I error rates and powers of the test are performed by simulation studies. Some examples will be illustrated the implementation of the test.

Keywords: case-control studies, goodness-of-fit test, Kolmogorov-Smirnov test, multinomial logistic regression

Procedia PDF Downloads 356
3890 Analyzing Large Scale Recurrent Event Data with a Divide-And-Conquer Approach

Authors: Jerry Q. Cheng

Abstract:

Currently, in analyzing large-scale recurrent event data, there are many challenges such as memory limitations, unscalable computing time, etc. In this research, a divide-and-conquer method is proposed using parametric frailty models. Specifically, the data is randomly divided into many subsets, and the maximum likelihood estimator from each individual data set is obtained. Then a weighted method is proposed to combine these individual estimators as the final estimator. It is shown that this divide-and-conquer estimator is asymptotically equivalent to the estimator based on the full data. Simulation studies are conducted to demonstrate the performance of this proposed method. This approach is applied to a large real dataset of repeated heart failure hospitalizations.

Keywords: big data analytics, divide-and-conquer, recurrent event data, statistical computing

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3889 Comparison between Some of Robust Regression Methods with OLS Method with Application

Authors: Sizar Abed Mohammed, Zahraa Ghazi Sadeeq

Abstract:

The use of the classic method, least squares (OLS) to estimate the linear regression parameters, when they are available assumptions, and capabilities that have good characteristics, such as impartiality, minimum variance, consistency, and so on. The development of alternative statistical techniques to estimate the parameters, when the data are contaminated with outliers. These are powerful methods (or resistance). In this paper, three of robust methods are studied, which are: Maximum likelihood type estimate M-estimator, Modified Maximum likelihood type estimate MM-estimator and Least Trimmed Squares LTS-estimator, and their results are compared with OLS method. These methods applied to real data taken from Duhok company for manufacturing furniture, the obtained results compared by using the criteria: Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE) and Mean Sum of Absolute Error (MSAE). Important conclusions that this study came up with are: a number of typical values detected by using four methods in the furniture line and very close to the data. This refers to the fact that close to the normal distribution of standard errors, but typical values in the doors line data, using OLS less than that detected by the powerful ways. This means that the standard errors of the distribution are far from normal departure. Another important conclusion is that the estimated values of the parameters by using the lifeline is very far from the estimated values using powerful methods for line doors, gave LTS- destined better results using standard MSE, and gave the M- estimator better results using standard MAPE. Moreover, we noticed that using standard MSAE, and MM- estimator is better. The programs S-plus (version 8.0, professional 2007), Minitab (version 13.2) and SPSS (version 17) are used to analyze the data.

Keywords: Robest, LTS, M estimate, MSE

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3888 Bayesian Reliability of Weibull Regression with Type-I Censored Data

Authors: Al Omari Moahmmed Ahmed

Abstract:

In the Bayesian, we developed an approach by using non-informative prior with covariate and obtained by using Gauss quadrature method to estimate the parameters of the covariate and reliability function of the Weibull regression distribution with Type-I censored data. The maximum likelihood seen that the estimators obtained are not available in closed forms, although they can be solved it by using Newton-Raphson methods. The comparison criteria are the MSE and the performance of these estimates are assessed using simulation considering various sample size, several specific values of shape parameter. The results show that Bayesian with non-informative prior is better than Maximum Likelihood Estimator.

Keywords: non-informative prior, Bayesian method, type-I censoring, Gauss quardature

Procedia PDF Downloads 405
3887 Model Averaging in a Multiplicative Heteroscedastic Model

Authors: Alan Wan

Abstract:

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

Procedia PDF Downloads 252
3886 Bayesian Using Markov Chain Monte Carlo and Lindley's Approximation Based on Type-I Censored Data

Authors: Al Omari Moahmmed Ahmed

Abstract:

These papers describe the Bayesian Estimator using Markov Chain Monte Carlo and Lindley’s approximation and the maximum likelihood estimation of the Weibull distribution with Type-I censored data. The maximum likelihood method can’t estimate the shape parameter in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions cannot be solved analytically. Hence Markov Chain Monte Carlo method and Lindley’s approximation are used, where the full conditional distribution for the parameters of Weibull distribution are obtained via Gibbs sampling and Metropolis-Hastings algorithm (HM) followed by estimate the survival and hazard functions. The methods are compared to Maximum Likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in scale and shape parameters, the survival and hazard functions.

Keywords: weibull distribution, bayesian method, markov chain mote carlo, survival and hazard functions

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3885 Efficient Estimation for the Cox Proportional Hazards Cure Model

Authors: Khandoker Akib Mohammad

Abstract:

While analyzing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest, and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using the cure model, which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package, and we compare the results with the output obtained from the SMCURE package.

Keywords: Cox PH model, cure model, efficient score function, EM algorithm, implicit function, profile likelihood

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3884 Parameter Estimation for the Mixture of Generalized Gamma Model

Authors: Wikanda Phaphan

Abstract:

Mixture generalized gamma distribution is a combination of two distributions: generalized gamma distribution and length biased generalized gamma distribution. These two distributions were presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation – maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β, λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 10, 30, 100; the simulations were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm.

Keywords: conjugate gradient method, quasi-Newton method, EM-algorithm, generalized gamma distribution, length biased generalized gamma distribution, maximum likelihood method

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3883 Robust Inference with a Skew T Distribution

Authors: M. Qamarul Islam, Ergun Dogan, Mehmet Yazici

Abstract:

There is a growing body of evidence that non-normal data is more prevalent in nature than the normal one. Examples can be quoted from, but not restricted to, the areas of Economics, Finance and Actuarial Science. The non-normality considered here is expressed in terms of fat-tailedness and asymmetry of the relevant distribution. In this study a skew t distribution that can be used to model a data that exhibit inherent non-normal behavior is considered. This distribution has tails fatter than a normal distribution and it also exhibits skewness. Although maximum likelihood estimates can be obtained by solving iteratively the likelihood equations that are non-linear in form, this can be problematic in terms of convergence and in many other respects as well. Therefore, it is preferred to use the method of modified maximum likelihood in which the likelihood estimates are derived by expressing the intractable non-linear likelihood equations in terms of standardized ordered variates and replacing the intractable terms by their linear approximations obtained from the first two terms of a Taylor series expansion about the quantiles of the distribution. These estimates, called modified maximum likelihood estimates, are obtained in closed form. Hence, they are easy to compute and to manipulate analytically. In fact the modified maximum likelihood estimates are equivalent to maximum likelihood estimates, asymptotically. Even in small samples the modified maximum likelihood estimates are found to be approximately the same as maximum likelihood estimates that are obtained iteratively. It is shown in this study that the modified maximum likelihood estimates are not only unbiased but substantially more efficient than the commonly used moment estimates or the least square estimates that are known to be biased and inefficient in such cases. Furthermore, in conventional regression analysis, it is assumed that the error terms are distributed normally and, hence, the well-known least square method is considered to be a suitable and preferred method for making the relevant statistical inferences. However, a number of empirical researches have shown that non-normal errors are more prevalent. Even transforming and/or filtering techniques may not produce normally distributed residuals. Here, a study is done for multiple linear regression models with random error having non-normal pattern. Through an extensive simulation it is shown that the modified maximum likelihood estimates of regression parameters are plausibly robust to the distributional assumptions and to various data anomalies as compared to the widely used least square estimates. Relevant tests of hypothesis are developed and are explored for desirable properties in terms of their size and power. The tests based upon modified maximum likelihood estimates are found to be substantially more powerful than the tests based upon least square estimates. Several examples are provided from the areas of Economics and Finance where such distributions are interpretable in terms of efficient market hypothesis with respect to asset pricing, portfolio selection, risk measurement and capital allocation, etc.

Keywords: least square estimates, linear regression, maximum likelihood estimates, modified maximum likelihood method, non-normality, robustness

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3882 The Generalized Pareto Distribution as a Model for Sequential Order Statistics

Authors: Mahdy ‎Esmailian, Mahdi ‎Doostparast, Ahmad ‎Parsian

Abstract:

‎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

Procedia PDF Downloads 415
3881 Practical Techniques of Improving State Estimator Solution

Authors: Kiamran Radjabli

Abstract:

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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3880 Bayes Estimation of Parameters of Binomial Type Rayleigh Class Software Reliability Growth Model using Non-informative Priors

Authors: Rajesh Singh, Kailash Kale

Abstract:

In this paper, the Binomial process type occurrence of software failures is considered and failure intensity has been characterized by one parameter Rayleigh class Software Reliability Growth Model (SRGM). The proposed SRGM is mathematical function of parameters namely; total number of failures i.e. η-0 and scale parameter i.e. η-1. It is assumed that very little or no information is available about both these parameters and then considering non-informative priors for both these parameters, the Bayes estimators for the parameters η-0 and η-1 have been obtained under square error loss function. The proposed Bayes estimators are compared with their corresponding maximum likelihood estimators on the basis of risk efficiencies obtained by Monte Carlo simulation technique. It is concluded that both the proposed Bayes estimators of total number of failures and scale parameter perform well for proper choice of execution time.

Keywords: binomial process, non-informative prior, maximum likelihood estimator (MLE), rayleigh class, software reliability growth model (SRGM)

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3879 Ratio Type Estimators for the Estimation of Population Coefficient of Variation under Two-Stage Sampling

Authors: Muhammad Jabbar

Abstract:

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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3878 A New Distribution and Application on the Lifetime Data

Authors: Gamze Ozel, Selen Cakmakyapan

Abstract:

We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of real life data set.

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood

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3877 Selection of Appropriate Classification Technique for Lithological Mapping of Gali Jagir Area, Pakistan

Authors: Khunsa Fatima, Umar K. Khattak, Allah Bakhsh Kausar

Abstract:

Satellite images interpretation and analysis assist geologists by providing valuable information about geology and minerals of an area to be surveyed. A test site in Fatejang of district Attock has been studied using Landsat ETM+ and ASTER satellite images for lithological mapping. Five different supervised image classification techniques namely maximum likelihood, parallelepiped, minimum distance to mean, mahalanobis distance and spectral angle mapper have been performed on both satellite data images to find out the suitable classification technique for lithological mapping in the study area. Results of these five image classification techniques were compared with the geological map produced by Geological Survey of Pakistan. The result of maximum likelihood classification technique applied on ASTER satellite image has the highest correlation of 0.66 with the geological map. Field observations and XRD spectra of field samples also verified the results. A lithological map was then prepared based on the maximum likelihood classification of ASTER satellite image.

Keywords: ASTER, Landsat-ETM+, satellite, image classification

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3876 On the Performance of Improvised Generalized M-Estimator in the Presence of High Leverage Collinearity Enhancing Observations

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

Abstract:

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

Procedia PDF Downloads 155
3875 Exponentiated Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution

Authors: Abd El Hady N. Ebraheim

Abstract:

This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: exponentiated, inversion method, maximum likelihood estimation, transmutation map

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3874 The Beta-Fisher Snedecor Distribution with Applications to Cancer Remission Data

Authors: K. A. Adepoju, O. I. Shittu, A. U. Chukwu

Abstract:

In this paper, a new four-parameter generalized version of the Fisher Snedecor distribution called Beta- F distribution is introduced. The comprehensive account of the statistical properties of the new distributions was considered. Formal expressions for the cumulative density function, moments, moment generating function and maximum likelihood estimation, as well as its Fisher information, were obtained. The flexibility of this distribution as well as its robustness using cancer remission time data was demonstrated. The new distribution can be used in most applications where the assumption underlying the use of other lifetime distributions is violated.

Keywords: fisher-snedecor distribution, beta-f distribution, outlier, maximum likelihood method

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3873 Adaptive Target Detection of High-Range-Resolution Radar in Non-Gaussian Clutter

Authors: Lina Pan

Abstract:

In non-Gaussian clutter of a spherically invariant random vector, in the cases that a certain estimated covariance matrix could become singular, the adaptive target detection of high-range-resolution radar is addressed. Firstly, the restricted maximum likelihood (RML) estimates of unknown covariance matrix and scatterer amplitudes are derived for non-Gaussian clutter. And then the RML estimate of texture is obtained. Finally, a novel detector is devised. It is showed that, without secondary data, the proposed detector outperforms the existing Kelly binary integrator.

Keywords: non-Gaussian clutter, covariance matrix estimation, target detection, maximum likelihood

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3872 Statistical Inferences for GQARCH-It\^{o} - Jumps Model Based on The Realized Range Volatility

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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3871 The Linear Combination of Kernels in the Estimation of the Cumulative Distribution Functions

Authors: Abdel-Razzaq Mugdadi, Ruqayyah Sani

Abstract:

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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3870 A Flexible Pareto Distribution Using α-Power Transformation

Authors: Shumaila Ehtisham

Abstract:

In Statistical Distribution Theory, considering an additional parameter to classical distributions is a usual practice. In this study, a new distribution referred to as α-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution including explicit expressions for the moment generating function, mode, quantiles, entropies and order statistics are obtained. Unknown parameters have been estimated by using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that α-Power Pareto distribution outperforms while compared to different variants of Pareto distribution on the basis of model selection criteria.

Keywords: α-power transformation, maximum likelihood estimation, moment generating function, Pareto distribution

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3869 Efficient Schemes of Classifiers for Remote Sensing Satellite Imageries of Land Use Pattern Classifications

Authors: S. S. Patil, Sachidanand Kini

Abstract:

Classification of land use patterns is compelling in complexity and variability of remote sensing imageries data. An imperative research in remote sensing application exploited to mine some of the significant spatially variable factors as land cover and land use from satellite images for remote arid areas in Karnataka State, India. The diverse classification techniques, unsupervised and supervised consisting of maximum likelihood, Mahalanobis distance, and minimum distance are applied in Bellary District in Karnataka State, India for the classification of the raw satellite images. The accuracy evaluations of results are compared visually with the standard maps with ground-truths. We initiated with the maximum likelihood technique that gave the finest results and both minimum distance and Mahalanobis distance methods over valued agriculture land areas. In meanness of mislaid few irrelevant features due to the low resolution of the satellite images, high-quality accord between parameters extracted automatically from the developed maps and field observations was found.

Keywords: Mahalanobis distance, minimum distance, supervised, unsupervised, user classification accuracy, producer's classification accuracy, maximum likelihood, kappa coefficient

Procedia PDF Downloads 100
3868 The Reproducibility and Repeatability of Modified Likelihood Ratio for Forensics Handwriting Examination

Authors: O. Abiodun Adeyinka, B. Adeyemo Adesesan

Abstract:

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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3867 Efficient Principal Components Estimation of Large Factor Models

Authors: Rachida Ouysse

Abstract:

This paper proposes a constrained principal components (CnPC) estimator for efficient estimation of large-dimensional factor models when errors are cross sectionally correlated and the number of cross-sections (N) may be larger than the number of observations (T). Although principal components (PC) method is consistent for any path of the panel dimensions, it is inefficient as the errors are treated to be homoskedastic and uncorrelated. The new CnPC exploits the assumption of bounded cross-sectional dependence, which defines Chamberlain and Rothschild’s (1983) approximate factor structure, as an explicit constraint and solves a constrained PC problem. The CnPC method is computationally equivalent to the PC method applied to a regularized form of the data covariance matrix. Unlike maximum likelihood type methods, the CnPC method does not require inverting a large covariance matrix and thus is valid for panels with N ≥ T. The paper derives a convergence rate and an asymptotic normality result for the CnPC estimators of the common factors. We provide feasible estimators and show in a simulation study that they are more accurate than the PC estimator, especially for panels with N larger than T, and the generalized PC type estimators, especially for panels with N almost as large as T.

Keywords: high dimensionality, unknown factors, principal components, cross-sectional correlation, shrinkage regression, regularization, pseudo-out-of-sample forecasting

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