Asymptotically most powerful rank tests for regression parameters in manova
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Srivastava  proposed a class of rank score tests for testing the hypothesis that β1=⋯β p =0 in the linear regression modely i =β1 x 1i +β2 x 2i +⋯+β p +x pi +ɛ i under weaker conditions than Hájek . In this paper, under the same weak conditions, a class of rank score tests is proposed for testing β1=⋯β q =0 in the multivariate linear regression modely i =β1 x 1i +β2 x 2i +⋯+β p +x pi +ɛ i ,q≦p, where β i ’s arek-vectors. The limiting distribution of the test statistic is shown to be central χ qk 2 underH and non-central χ qk 2 under a sequence of alternatives tending to the hypothesis at a suitable rate.
KeywordsRandom Matrix Suitable Rate Rank Order Test Score Test Statistic Contiguity Principle
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- Srivastava, M. S. (1968). On a class of non-parametric tests for regression parameters (abstract),Ann. Math. Statist.,39, 697.Google Scholar