Parameter Estimation Methods in Multiple Linear Regression Analysis with Autocorrelation and Heavy-Tailed Distributed Data

Abstract

Regression analysis is extensively used in a wide variety of fields, especially for predictive purpose. Its assumptions play a crucial role in parameter estimation. This paper focuses on parameter estimation in multiple linear regression when the assumptions are violated with simultaneous presence of autocorrelated random errors of AR(1) structure and heavy-tailed distribution, using hierarchical Bayes approach, which prior information about parameters, both noninformative and informative priors, is incorporated into the model. The result is also compared with frequently used method, maximum likelihood estimation, using the mean square error (MSE) as a criterion for comparison. The result reveals that hierarchical Bayes with informative priors outperform the maximum likelihood method, yielding the smallest MSEs for all sample sizes and correlation coefficients. Keywords: Autocorrelation, Heavy-tailed distribution, Maximum likelihood, Hierarchical Bayes