Abstract
In this study we consider a multivariate one-sided test for testing whether a normal mean vector having nonnegative components is equal to zero or not under the assumption that the covariance matrix is known. First, we discuss Kudo (1963)'s method based on the likelihood ratio test. Next, we discuss Tang et al. (1989)'s simple method which is called the approximate likelihood ratio test for the multivariate one-sided test. Furthermore, we discuss Glimm et al. (2002)'s method which modifies Tang et al. (1989)'s method. Specifically, we have two kinds of approximate methods for Kudo (1963)'s likelihood ratio test. We compare them in terms of numerical examples regarding critical values and power of the test.
