ON THE POWER FUNCTION OF THE LRT AGAINST ONE-SIDED AND TWO-SIDED ALTERNATIVES IN BIVARIATE NORMAL DISTRIBUTION

Abstract

This paper addresses the problem of testing simple hypotheses about the mean of a bivariate normal distribution with identity covariance matrix against restricted alternatives. The LRTs and their power functions for such types of hypotheses are derived. Furthermore, through some elementary calculus, it is shown that the power function of the LRT satisfies certain monotonicity and symmetry properties. We treat two cases, the case of one-sided alternatives restricted to some closed convex cone, and the case of two-sided alternatives restricted to a two-sided cone