Journal of Statistical Sciences

The Bayesian Wavelet Thresholding Estimators of Nonparametric Regression Model Based on Mixture Prior Distribution

Abouzar Bazyari

In this paper, the wavelet estimators of the nonparametric regression function based on the various thresholds under the mixture prior distribution and the mean square error loss function in Bosove space are computed. Also, using a simulation study the optimality of different wavelet thresholding estimators such as posterior mean, posterior median, Bayes factor, universal threshold and sure threshold are investigated. The results show that the average mean square error of sure threshold estimator is less than the other obtained estimators.

Bayesian Analysis of Spatial Count Data in Finite Populations Using Stochastic Partial Differential Equations

Hossein Baghishani

Geostatistical spatial count data in finite populations can be seen in many applications, such as urban management and medicine. The traditional model for analyzing these data is the spatial logit-binomial model. In the most applied situations, these data have overdispersion alongside the spatial variability. The binomial model is not the appropriate candidate to account for the overdispersion. The proper alternative is a beta-binomial model that has sufficient flexibility to account for the extra variability due to the possible overdispersion of counts. In this paper, we describe a Bayesian spatial beta-binomial for geostatistical count data by using a combination of the integrated nested Laplace approximation and the stochastic partial differential equations methods. We apply the methodology for analyzing the number of people injured/killed in car crashes in Mashhad, Iran. We further evaluate the performance of the model using a simulation study.

Likelihood Ratio Ordering of k-out-of-n Systems Comprising Multiple-outlier Scale Components

Ebrahim Amini Seresht

This paper examines the problem of stochastic comparisons of k-out-of-n systems with independent multiple-outlier scale components. In this regard, we first consider a k-out-of-n system comprising multiple-outlier scale components and then, by using a permanent function, investigate the likelihood ratio order between these systems.

Optimization of Reliability and Cost in Series-Parallel-Repairable Systems with Bathtub-Shaped Failure Rate

Elham Basiri

When a system is used, it is often of interest to determine with what probability it will work longer than a pre-fixed time. In other words, determining the reliability of this system is of interest. On the other hand, the reliability of each system depends on the structure and reliability of its components. Therefore, in order to improve the reliability of the system, the reliability of its components should be improved. For this purpose, it is necessary to carry out maintenance operations, which will increase costs. Another way to increase the reliability of systems is to change the location of the components. In this paper, the location of system components and optimal maintenance period are determined by minimizing the costs and maximizing the reliability of a series-parallel system. Finally, a numerical example is presented to evaluate the results in the paper.

Variable Selection in Semiparametric Mixed Effect Model for High-Dimension Longitudinal Data

Mozhgan Taavoni

This paper considers the problem of simultaneous variable selection and estimation in a semiparametric mixed-effects model for longitudinal data with normal errors. We approximate the nonparametric function by regression spline and simultaneously estimate and select the variables under the optimization of the penalized objective function. Under some regularity conditions, the asymptotic behaviour of the resulting estimators is established in a high-dimensional framework where the number of parametric covariates increases as the sample size increases. For practical implementation, we use an EM algorithm to selects the significant variables and estimates the nonzero coefficient functions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed to illustrate the proposed procedure.

Inaccuracy Measure Based on Survival Copula

Seyede Toktam Hosseini

In this paper, using the idea of inaccuracy measure in the information theory, the residual and past inaccuracy measures in the bivariate case are defined based on copula functions. Under the assumption of radial symmetry, the equality of these two criteria is shown, also by the equality between these two criteria, radially symmetrical models are characterized. A useful bound is provided by establishing proportional (inverse) hazard rate models for marginal distributions. Also, the proportional hazard rate model in bivariate mode is characterized by assuming proportionality between the introduced inaccuracy and its corresponding entropy. In addition, orthant orders are used to obtain inequalities. To illustrate the results, some examples and simulations are presented.

Modeling of Chronological Age Using Least Trimmed Squares Ridge Regression

Mahdi Roozbeh

The popular method to estimation the parameters of a linear regression model is the ordinary least square method which, despite the simplicity of calculating and providing the BLUE estimator of parameters, in some situations leads to misleading solutions. For example, we can mention the problems of multi-collinearity and outliers in the data set. The least trimmed squares method which is one of the most popular of robust regression methods decreases the influence of outliers as much as possible. The main goal of this paper is to provide a robust ridge estimation in order to model dental age data. Among the methods used to determine age, the most popular method throughout the world is the modern modified Demirjian method that is based on the calcification of the permanent tooth in panoramic radiography. It has been shown that using the robust ridge estimator is leading to reduce the mean squared error in comparison with the OLS method. Also, the proposed estimators were evaluated in simulated data sets.

Bayes and Empirical Bayesian Estimator of Reliability Function in Multicomponent Stress-Strength System based on Generalized Rayleigh Distribution

Reza Zarei

In this paper, the Bayesian and empirical Bayesian approaches studied in estimate the multicomponent stress–strength reliability model when the strength and stress variables have a generalized Rayleigh distribution with different shape parameters and identical scale parameter. The Bayesian, empirical Bayesian and maximum likelihood estimation of reliability function is obtained in the two cases known and unknown of scale parameter under the mean squared error loss function. Then, these estimators are compared empirically using Monte Carlo simulation and two real data sets.

The Convolution of Multivariate Normal and Standard Exponential Distributions: Theory and Application

Mohsen Madadi

In this article, a mixture of multivariate normal and standard exponential distributions is investigated. It is shown that the range of skewness and kurtosis coefficients for this distribution is wider than that of the skew-normal distribution. Some properties of this distribution, such as characteristic function, moment generating function, four first moments, skewness and kurtosis of distribution are presented. Also, the distribution of offine transformations and canonical forms of distribution are derived. The maximum likelihood estimation of parameters of the model is computed by using an EM algorithm. To investigate the suitability and efficiency of the model, a simulation study is presented. Finally, two numerical examples with real data sets are studied.

Inference of Common Correlation Coefficient Based on Confidence Distribution Concept

Mohammad Reaz Kazemi

In this paper, we investigate the confidence interval for the parameter of the common correlation coefficient of several bivariate normal populations. To do this, we use the confidence distribution approach. By simulation studies and using the concepts of coverage probability and expected length, We compare this method with the generalized variable approach. Results of simulation studies show that the coverage probability of the proposed method is close to the nominal level in all situations and also, in most cases, the expected length of this method is less than that of the generalized variable approach. Finally, we present two real examples to apply this approach.

The Analysis of Weibull Lifetime Data Subject to Imperfect Repair

Javad Etminan

A repairable system with two types of failures is studied. Type I failure (minor failure) is removed by a minimal repair, whereas type II failure (catastrophic failure) is modified by an unplanned replacement. The first failure of the system follows a Weibull probability distribution and two maintenance policies are considered. In the first policy, the system is replaced at time T or the first type II failure, and in the second policy, the system is replaced at the nth type I failure, the first type II failure or at time T, whichever takes place first. This paper aims to derive a general representation for the likelihood function of the proposed models. The likelihood-ratio test statistic, maximum likelihood estimators and asymptotic confidence intervals for the parameters are also found. Finally, a Monte Carlo simulation is conducted to illustrate the results.

Bayesian Estimation of Stress-Strength Parameter under Progressive Hybrid Censored Sample in Lomax Distribution

Akram Kohansal

The Bayesian estimation of the stress-strength parameter in Lomax distribution under the progressive hybrid censored sample is considered in three cases. First, assuming the stress and strength are two random variables with a common scale and different shape parameters. The Bayesian estimations of these parameters are approximated by Lindley method and the Gibbs algorithm. Second, assuming the scale parameter is known, the exact Bayes estimation of the stress-strength parameter is obtained. Third, assuming all parameters are unknown, the Bayesian estimation of the stress-strength parameter is derived via the Gibbs algorithm. Also, the maximum likelihood estimations are calculated, and the usefulness of the Bayesian estimations is confirmed, in comparison with them. Finally, the different methods are evaluated utilizing the Monte Carlo simulation and one real data set is analyzed.

The Population Mean Estimators by using Judgment Post Stratification in Stratified Sampling

Nader Nematollahi

Judgment post-stratification is a method of using additional information of ranking in the simple random sampling, to increase the efficiency of the estimators of population parameters. In this paper, we use judgment post-stratification instead of simple random sampling in stratums of stratified sampling, and present new estimators for population mean. Then, we compare the proposed estimators with random stratified mean estimator by using a simulation study. The simulation results show that the proposed estimators perform better than the random stratified mean estimator in most of the cases.

A Class of Bayesian Shrinkage Estimators for the Scale Parameter of Weibull Distribution Based on Censored Data

Mehran Naghizadeh Qomi

In classical statistics, the parameter of interest is estimated based on sample information and using natural estimators such as maximum likelihood estimators. In Bayesian statistics, the Bayesian estimators are constructed based on prior knowledge and combining with it sample information. But, in some situations, the researcher has information about the unknown parameter as a guess. Bayesian shrinkage estimators can be constructed by Combining this non-sample information with sample information together with the prior knowledge, which is in the area of semi-classical statistics. In this paper, we introduce a class of Bayesian shrinkage estimators for the Weibull scale parameter as a generalization of the estimator at hand and consider the bias and risk of them under LINEX loss function. Then, the proposed estimators are compared using a real data set.