Conditional Likelihood Ratio Test for a Nonnegative Normal Mean Vector

Abstract

The conditional likelihood ratio test is derived for significance of a multivariate mean having nonnegative components. This test is shown to be uniformly more powerful than the unconditional likelihood ratio test derived by Perlman. The computation involved in the new test is a straightforward programming task. Simulation results suggest that this test is also uniformly more powerful than a half-space test proposed by Tang and Hotelling's T 2 test. The consistency, invariance and unbiasedness of the new test are established, and the test is illustrated with data from a randomized clinical trial.