On the size corrected tests in improved estimation

In this paper we propose shrinkage preliminarytest estimator (SPTE) of the coefficient vector in the multiplelinear 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 offreedom corrections to the estimate of the error variance andthose obtained from the second-order Edgeworth approximations tothe exact distributions of the test statistics. The bias andweighted mean squared error (WMSE) functions of the estimators arederived. With respect to WMSE, the relative efficiencies of theSPTEs relative to the maximum likelihood estimator are calculated.This study shows that the amount of conflict can be substantialwhen the three tests are based on the same asymptotic chi-squarecritical value. The conflict among the SPTEs is due to theasymptotic tests not having the correct significance level. TheEdgeworth size corrected W, LR and LM tests reduce theconflict remarkably.