On the size corrected tests in improved estimation

Abstract

In this paper we propose shrinkage preliminary test estimator (SPTE) of the coefficient vector in the multiple linear regression model based on the size corrected Wald (W), likelihood ratio (LR) and Lagrangian multiplier (LM) tests. The correction factors used are those obtained from degrees of freedom corrections to the estimate of the error variance and those obtained from the second-order Edgeworth approximations to the exact distributions of the test statistics. The bias and weighted mean squared error (WMSE) functions of the estimators are derived. With respect to WMSE, the relative efficiencies of the SPTEs relative to the maximum likelihood estimator are calculated. This study shows that the amount of conflict can be substantial when the three tests are based on the same asymptotic chi-square critical value. The conflict among the SPTEs is due to the asymptotic tests not having the correct significance level. The Edgeworth size corrected W, LR and LM tests reduce the conflict remarkably.