Ridge estimation in semi-parametric regression models under the stochastic restriction and correlated elliptically contoured errors

Abstract

Some linear stochastic constraints may occur during real data set modeling, based on either additional information or prior knowledge. These stochastic constraints often cause some changes in the behaviors of estimators. In this research, shrinkage ridge estimators as well as their positive parts are proposed in the semi-parametric model when some stochastic constrains are imposed under a multicollinearity setting. Also, it is assumed that the error terms are dependent and distributed according to the elliptically contoured models. The bias and risk expressions of the proposed estimators for comparison purposes are derived. Finally, the Monte-Carlo simulation studies and a real application related to electricity consumption data are conducted to support our theoretical discussion.