Search

In this study, we introduce a matrix variate skew Laplace distribution as a variance-mean mixture of the matrix variate normal and the scale inverse gamma distribution. The proposed distribution is a generalization of the multivariate skew Laplace distribution studied by [1]. We explore some distributional properties of the proposed distribution such as the probability density function and the characteristic function. Also, we study the estimation of the parameters and give an EM algorithm to obtain the estimates of the parameters. Then, we give a small simulation study to illustrate the performance of the proposed EM algorithm for finding the estimates. [ABSTRACT FROM AUTHOR]

Modelling skewness and heavy-tailedness in heterogeneous data sets is a compelling problem, particularly in regression analysis. The main goal of this study is to propose a mixture regression model based on the shape mixtures of skew Laplace normal (SMSLN) distribution for modelling skewness and heavy-tailedness simultaneously. The SMSLN distribution has been introduced by Doğru and Arslan [Finite mixtures of skew Laplace normal distributions with random skewness. 11th International Statistics Congress (ISC2019); Bodrum/Turkey; Finite mixtures of skew Laplace normal distributions with random skewness. Comput Stat. 2021;36(1):423–447] as a flexible extension of the skew Laplace normal (SLN) distribution and includes an extra shape parameter that controls skewness and kurtosis. The maximum likelihood estimators for the parameters of interest with the help of the expectation-maximization (EM) algorithm are obtained. The performance of the proposed mixture model is demonstrated via a simulation study and a real data example. [ABSTRACT FROM AUTHOR]

This article aims to determine the features affecting the price of a product with the hedonic regression model and to estimate the contribution of each feature to the price by using robust regression estimation methods. For the analysis, the price and feature information of the laptop product group were obtained from the big data source by using the web scraping method. Four alternatives of the hedonic regression model are used to determine the features affecting the price of the laptops. The contribution of each feature to the laptop price is estimated by using the robust (Huber M-estimator) estimation method and the Ordinary Least Squares (OLS) estimation method, and the resulting estimates are compared for both methods. In the framework of the data set used in the study, it is observed that the effective model is the Logarithmic Robust Hedonic Regression Model. [ABSTRACT FROM AUTHOR]

Linear regression models are useful statistical tools to analyze data sets in different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally distributed and uncorrelated errors. If error terms are correlated the Conditional Maximum Likelihood (CML) estimation method under normality assumption is often used to estimate the parameters of interest. The CML estimation method is required a distributional assumption on error terms. However, in practice, such distributional assumptions on error terms may not be plausible. In this paper, we propose to estimate the parameters of a linear regression model with autoregressive error term using Empirical Likelihood (EL) method, which is a distribution free estimation method. A small simulation study is provided to evaluate the performance of the proposed estimation method over the CML method. The results of the simulation study show that the proposed estimators based on EL method are remarkably better than the estimators obtained from CML method in terms of mean squared errors (MSE) and bias in almost all the simulation configurations. These findings are also confirmed by the results of the numerical and real data examples. [ABSTRACT FROM AUTHOR]

Ordinary least square (OLS) and robust methods are used for estimating the parameters of a linear regression model. These methods perform well under some distributional assumptions which may not be appropriate for some data sets. Therefore, nonparametric methods like Empirical likelihood (EL) may be considered. The EL method maximizes an EL function under some constraints. We consider the EL method with robustified constraints using M estimation method. We provide a small simulation study and a real data example to demonstrate the capability of robust EL method and results reveal that robust constraints are needed when outliers are resent in data. [ABSTRACT FROM AUTHOR]

Linear regression is a well-known method to predict further values for dependent variable given observed independent variables. Sometimes, there is prior information about regression coefficients. Therefore, restricted regression takes into account prior information and combines it with the sample information. Unfortunately, restricted regression has same assumptions as a linear regression. In this paper, we propose robust estimation of restricted linear models. In the application part, it is demonstrated that the proposed methods are convenient method to give impressive results in the presence of outliers with stochastic or nonstochastic restriction. [ABSTRACT FROM AUTHOR]