Parameter estimation methods in multiple linear regression analysis with intraclass correlation and heavy-tailed distributed data

Abstract

The underlying assumptions play an important role in the linear regression analysis. Non-validity of assumptions can cause the estimators of regression coefficients no longer possessing the properties of best linear unbiased estimator (BLUE). This research focuses on parameter estimation in regression model when random errors are correlated with intraclass correlation and followed heavy-tailed distribution simultaneously. Alternative to searching for techniques to remedy the problem of violation, hierarchical Bayes approach is implemented to estimate model parameter, in which prior knowledge about parameters is incorporated to reduce the effect of violated assumptions. Its performance is then compared to the classical approach, maximum likelihood (ML), through Monte Carlo simulation. The study indicates that hierarchical Bayes with informative priors yields the estimators more efficient than ML.