PROJECTED TESTS FOR ORDER RESTRICTED ALTERNATIVES

• 成果类型: Article
• 署名作者: COHEN, A; KEMPERMAN, JHB; SACKROWITZ, HB
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325641
• 发表日期: 1994
• 页码: 1539-1546
• 关键词: homogeneity

摘要

Consider the model where X(ij), i = 1, 2,..., k, j = 1, 2,..., n, are independent random variables distributed according to a one-parameter exponential family with natural parameter theta(i). We test H-0: theta(1) =... = theta(k) versus H-1: theta is an element of C - {theta: theta is an element of H-0}, where theta = (theta(1),..., theta(k))' and C is a cone determined by A theta greater than or equal to 0, where the rows of A are contrasts with two nonzero elements. We offer a method of generating ''good'' tests for H-0 versus H-1. The method is to take a ''good'' test for H-0 versus H-2: not H-0, and apply the test to projected sample points, where the projection is onto e. ''Good'' tests for H-0 versus H-2 are tests that are Schur convex. ''Good'' tests for H-0 versus H-1 are tests which are monotone with respect to a cone order. We demonstrate that if the test function for H-0 versus H-2 is a constant size Schur convex test, then the resulting projected test is monotone.