Samruam Chongcharoen

pp. 351 - 359

Abstract

For a multivariate normal population, Kudo (1963), Shorack (1967) and Perlman (1969) derived the likelihood ratio tests of the null hypothesis that the mean vector is zero with a one-sided alternative for a known covariance matrix, a partially known covariance matrix and a completely unknown covariance matrix, respectively. Because these tests may be tedious to use, Tang, Gnecco and Geller (1989) developed approximate likelihood ratio tests and Follmann (1996) proposed one-sided
modifications of the usual omnibus chi-squared test and Hotelling’s T²
 test. Also, we consider a modification of Follmann’s test (the new test) to include information of off diagonal of covariance matrix , which adjusts for possibly unequal variances. For the non-normal population, Boyett and Shuster (1977) proposed a nonparametric one-sided test and we use their technique to develop nonparametric versions of Perlman’s test, Follmann’s test, the new test and the Tang-Gnecco-Geller test. Following Chongcharoen, Singh and Wright (2002), who considered known and partially known covariance matrices, we study the powers of these one-sided tests for an unknown covariance matrix using Monte Carlo techniques and make recommendations concerning their use. 

Keywords

• Follmann’s test
• Kudo’s test
• Perlman’s test
• Simple order
• Simple tree order
• Tang-Gnecco-Geller test and Boyett and Shuster test