p.1093

Minimax Regret Significance Points for a Preliminary Test in Regression Analysis

Takamitsu Sawa
Takeshi Hiromatsu

Abstract

The preliminary test estimator (or predictor) is studied in the context of linear normal regression models. The estimator (or predictor) obtained after the preliminary test is known to be inadmissible with respect to squared error loss under certain assumptions. Nevertheless, it is still widely used in practical application of regression analysis, particularly in econometrics. The object of the present paper is to tabulate the optimal significance points in the preliminary test for practical use. The optimality is based on the minimax regret principle. It is shown that if, as is usual, we take the significance point equal to the 5 per cent point or 10 per cent point, the risk is extremely large for some parameter value. The optimal significance point of the preliminary t test decreases slightly as the degrees of freedom increase,but it is nearly constant; i.e., it lies between 1.370 to 1.380 if d.f. is greater than 6.