Simulation study of new estimators combining the SUR ridge regression and the restricted least squares methodologies

Abstract

In this paper, we propose two SUR type estimators based on combining the SUR ridge regression and the restricted least squares methods. In the sequel these estimators are designated as the restricted ridge Liu estimator and the restricted ridge HK estimator (see Liu in Commun Statist Thoery Methods 22(2):393–402, 1993; Sarkar in Commun Statist A 21:1987–2000, 1992). The study has been made using Monte Carlo techniques, (1,000 replications), under certain conditions where a number of factors that may effect their performance have been varied. The performance of the proposed and some of the existing estimators are evaluated by means of the TMSE and the PR criteria. Our results indicate that the proposed SUR restricted ridge estimators based on KSUR, KSratio, KMratio and \({\ddot{K}}\) produced smaller TMSE and/or PR values than the remaining estimators. In contrast with other ridge estimators, components of \({\ddot{K}}\) are defined in terms of the eigenvalues of \({X^{{\ast^{\prime}}} X^{\rm \ast}}\) and all lie in the open interval (0, 1).