MSE Performance and Minimax Regret Significance Points for a HPT Estimator when each Individual Regression Coefficient is Estimated
Communications in Statistics - Theory and Methods
HAIFENG XU
Abstract: In this article, we consider a heterogeneous preliminary test (HPT) estimator whose components are the OLS and feasible ridge regression (FRR) estimators, and derive the exact formulae for the moments of the HPT estimator using mathematical method. Since we cannot examine the MSE of the HPT estimator analytically, we execute the numerical evaluation to investigate the MSE performance of the HPT estimator, and compare the MSE performance of the HPT estimator with those of the FRR estimator and the usual OLS estimator. Furthermore, using the minimax regret criterion proposed by Sawa and Hiromatsu (1973), we derive the optimal critical points of the preliminaryFtest. Our results show that the optimal significance points are greater than 19% and the optimal signicance points decrease as the denominator degrees of freedom of the preliminaryFtest statistic increases.
KeywordsFeasible ridge regression estimator; Heterogeneous preliminary test estimator; Minimax regret criterion; Optimal critical points.
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