Combining Alternative Rank Tests for the Multiple Regression Problem

In this paper we consider the problem of testing absence of regression under the nonparametric multiple regression set up with m predictors. Usual rank tests for this problem are based on particular systems of scores, the test criteria being quadratic forms in m linear rank statistics. Different standard tests correspond to different choices of the system of scores. In this paper we have proposed a test statistic which is based on the simultaneous choice of more than one system of scores. Asymptotic null distribution of the test criterion is a chisquare with m df as in the case of the usual tests. However, the use of several systems of scores results in the improvement of the asymptotic power over the test based on any one of the systems. Ofcourse the use of the test criterion in practice involves the estimation of indices involving the parent density f( . ). Certain standard estimates of these indices are noted in the last section.