Increasing power of robust test through pre-testing in multiple regression model

In this paper,we define (i) unrestricted (ut),(ii) restricted (rt) and (iii) pre-test (ptt) tests for testing the significance of a subset of the parameters of a multiple regression model when the remaining parameters are (i) completely unspecified,(ii) specified at fixed values or (iii) suspected at fixed values. the m-estimation methodology is used to formulate the three tests. the asymptotic distribution of the test statistics are used to derive the asymptotic power function of the tests. analytical and graphical comparisons of the three tests are obtained by studying the power functions with respect to the size and power of the tests. the ptt shows a reasonable dominance over the other two tests asymptotically. © 2010 pakistan journal of statistics.