Increasing power of the test through pre-test - a robust method

This paper develops robust test procedures for testing the intercept of a simple regression model when it is apriori suspected that the slope has a specified value. Defining unrestricted test (UT), restricted test (RT) and pre-test test (PTT) corresponding to the unrestricted (UE), restricted (RE), and preliminary test estimators (PTE) in the estimation case, the M-estimation methodology is used to formulate the M-tests and derive their asymptotic power functions. Analytical and graphical comparisons of the three tests are obtained by studying the power functions with respect to size and power of the tests. It is shown that PTT achieves a reasonable dominance over the others asymptotically.