DETERMINATION OF CRITICAL VALUE OF MULTIVARIATE NORMAL TEST WITH TWO-SIDED ALTERNATIVE BASED ON LIKELIHOOD RATIO TEST

When all components of a normal mean vector are simultaneously nonnegative or nonpositive, we consider a multivariate test for checking whether at least one component is nonzero based on the likelihood ratio test. First, we assume that the covariance matrix is known. Next, we assume that it is unknown. In both cases, we consider the determination of the critical value for a specified significance level. Since it is difficult to determine the distributions of the likelihood ratio test statistics, we obtain an approximate critical value using two methods, namely computation using grids and Monte Carlo integration. We give numerical examples regarding critical values intended to compare these methods.