Bayesian stein-type shrinkage estimators in high-dimensional linear regression models

In this study, we examine high-dimensional Bayesian linear regression based on a hierarchical model that places prior distributions on the regression coefficients along with a prior over model space. There is no closed-form expression for the posterior distribution on high-dimensional parameters; therefore, we use Markov Chain Monte Carlo methods to simulate the posterior distribution. Furthermore, we propose a stein-type shrinkage estimation strategy when it is suspected that some of the regression coefficients may be restricted to a linear subspace. The performance of the proposed methods based on a finite sample is demonstrated via real data analysis of Riboflavin production data and a Monte Carlo simulation study.