Variable Selection in Multivariate Linear Regression Models Subject to Sampling Errors

Abstract

In 2015, Lahiri and Suntornchost showed that sampling errors could cause bias in the variable selection criteria statistics in univariate linear regression models. In their study, they suggested ways to adjust those variable selection statistics to reduce the biasedness for the Fay-Herriot model when regression error terms are assumed to be independent and identically distributed. In this study, we will extend their methods to adjust the original variable selection criteria for multivariate linear regression model subject to sampling errors. Simulation results show that our proposed variable selection criteria can reduce the approximation errors of the standard variable selection criterion.