Bayesian Approach for Comparing Parameter Estimation of Regression Model for Outlier Data

Abstract

This research compares and contrasts the simple regression model's parameter estimation methods, which consisted of a dependent variable and one independent variable. Parameter estimation uses the ordinary least square method, Bayesian method, Markov Chain Monte Carlo (MCMC) method, and local weight Markov Chain Monte Carlo (LWMCMC) method. The standard method is the ordinary least square method, which uses the concept of minimum sum square error to estimate parameters for fitting the linear regression model. However, for a set of the parameter relating to the Bayesian approach, the use of prior and posterior distributions may affect the approximation of the Bayesian, MCMC, LWMCMC methods. This paper considers the ordinal least square method and Bayesian approach by estimating the parameter for outlier data while some data points are far from other observations. The independent variable is simulated from the contaminated normal distribution, and the error is simulated from the normal distribution that made the outlier data on dependent and independent variables for the several sample sizes as 20, 50, 100, and 200. The criterion of the best efficiency is considered by the minimum of the average mean square errors. Through simulation data, the Bayesian method presents the minimum of average mean square errors at the sample sizes 20 and 50. However, when the sample size value increases, the MCMC and LWMCMC method are the best efficiency method at the sample sizes 100 and 200, respectively.