Asymptotically most powerful rank tests for regression parameters in manova

  • M. S. Srivastava
Article

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 1 x 1i 2 x 2i +⋯+β p +x pi 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 1 x 1i 2 x 2i +⋯+β p +x pi 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.

Keywords

Random Matrix Suitable Rate Rank Order Test Score Test Statistic Contiguity Principle 

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References

  1. [1]
    Hájek, J. (1961). Some extensions of the Wald-Wolfivitz-Noether theorem,Ann. Math. Statist.,32, 506–523.MATHMathSciNetGoogle Scholar
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    Hájek, J. (1962). Asymptotically most powerful rank order tests,Ann. Math. Statist.,33, 1124–1147.MATHMathSciNetGoogle Scholar
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    LeCam, L. (1960). Locally asymptotic normal families of distributions,Univ. of California Publication,3, No. 2, 37–98.MATHMathSciNetGoogle Scholar
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    Srivastava, M. S. (1967). On fixed-width confidence bound for regression parameters and mean vector,J. R. Statist. Soc. B,29, 132–140.MATHGoogle Scholar
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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

Copyright information

© Institute of Statistical Mathematics 1972

Authors and Affiliations

  • M. S. Srivastava

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