Original Article | 2010, Vol.32, No.3, pp. 321-326
Scale invariant for one-sided multivariate likelihood ratio tests
Samruam Chongcharoen
pp. 321 - 326
Abstract
Suppose X1, X2, ,..., Xn is a random sample from N p(θ ,V) distribution. Consider H0 : θ1= θ2 =... = θp = 0 and H1: θi ≥ 0 for i = 1, 2,...,p , let H1 – H0 denote the hypothesis that H1 holds but H0 does not, and let ~ H0 denote the hypothesis that H0 does not hold. Because the likelihood ratio test (LRT) of H0 versus H1 – H0 is complicated, several ad hoc tests have been proposed. Tang, Gnecco and Geller (1989) proposed an approximate LRT, Follmann (1996) suggested rejecting H0 if the usual test of H0 versus ~ H0 rejects H0 with significance level 2∝ and a weighted sum of the sample means is positive, and Chongcharoen, Singh and Wright (2002) modified Follmann’s test to include information about the correlation structure in the sum of the sample means. Chongcharoen and Wright (2007, 2006) give versions of the TangGnecco-Geller tests and Follmann-type tests, respectively, with invariance properties. With LRT’s scale invariant desired property, we investigate its powers by using Monte Carlo techniques and compare them with the tests which we recommend in Chongcharoen and Wright (2007, 2006).
