Asymptotically most powerful rank tests for regression parameters in manova

Summary

Srivastava [5] 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 [2]. 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 ² _qk underH and non-central χ ² _qk under a sequence of alternatives tending to the hypothesis at a suitable rate.