Samruam Chongcharoen

pp. 321 - 326

Abstract

Suppose X₁, X₂, ,..., X_n
 is a random sample from N _p(θ ,V) distribution. Consider H₀ : θ₁= θ₂ =... = θ_p = 0 and
H₁: θ_i ≥ 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).