An approach to a one-sided test in the bivariate normal distribution

Abstract

SUMMARY In this paper we propose a new test procedure for a one-sided alternative concerning the mean vector in a bivariate normal population with known covariance matrix. The problem was investigated by Kudü (1963) with the likelihood ratio criterion, while our procedure is derived from a new principle. The principle will be useful for many testing problems. Monte Carlo results are given showing that our procedure is more powerful when the population correlation is negative. In addition, some discussions on the two-sided case and multivariate case are given.