Directional monotonicity properties of the power functions of likelihood ratio tests for cone-restricted hypotheses of normal means

In some cone-restricted testing problems, it is known that the power function of the likelihood ratio test has a certain monotonicity property with respect to the direction of the alternatives. In this paper, we establish a unified result concerning such directional monotonicity by using an argument based on a cone ordering and a related probability inequality. From this result, we show that the power function is unimodal in direction when the cone is suitably symmetric. (C) 1998 Elsevier Science B.V. All rights reserved.