A Note on Asymptotically Distribution Free Tests for Subhypotheses in Multiple Linear Regression

Abstract

The purpose of this note is to show that asymptotically distribution-free (ADF) rank tests proposed by Koul [Ann. Math. Statist. 41 (1970), 1273-1281] for testing subhypotheses in multiple linear regression when based on symmetric scores are asymptotically totally inefficient and can even be inconsistent for symmetric parent distributions. Also, the condition given in his Theorem 2.4 for a test to be ADF is not necessary.