Stein-type improvement under stochastic constraints: Use of multivariate Student-t model in regression

Abstract

Recently, many researchers have considered the use of heavy-tailed models for processing multiplicative economic and business data for validity of robustness. As a reliable justification, fat-tailed models contain outliers and extreme values reasonably well. In this paper, we assume in the multiple regression model, that the error vector follows multivariate Student-t distribution as a viable alternative to the multivariate normal and obtain unrestricted and restricted estimators under the suspicion of stochastic constraints occurring. Also the preliminary test, Stein-type shrinkage and positive-rule shrinkage estimators are derived when the variable term in the restriction is assumed to follow multivariate Student-t distribution. The conditions of superiority of the proposed estimators are provided under weighted quadratic loss function.