M-test for intercept after pre-testing on slope

Abstract

In the M-estimation methodology, a procedure was develop for testing the intercept after pre-testing on the slope (Yunus and Khan, in press). The (i) unrestricted test (UT), (ii) restricted test (RT) and (iii) pre-test test (PTT) on intercept defined when the non-sample prior information (NSPI) on the slope is (i) unknown, (ii) certain or (iii) uncertain are considered. This paper investigates the performance (size and power) of the UT, RT and PTT by introducing the coefficient of variation. It is shown that the PTT achieves a reasonable dominance over the other tests asymptotically and performs better for larger coefficient of variation.