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On a class of asymptotically optimal nonparametric tests for grouped data I

  • Malay Ghosh
Article

Summary

Generalizing the results of Sen [8], a class of nonparametric tests for the hypothesis of no regression in the multiple linear regression model is obtained here. The asymptotic power properties of the proposed class of tests are studied, and the asymptotic optimality of the tests is established under the conditions of Wald [10]. Applications of the results are also considered.

Keywords

Assumed Distribution Asymptotic Relative Efficiency Classical Central Limit Theorem Ungrouped Data True Distribution Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Basu, A. P. (1967). On twoK-sample rank tests for censored data,Ann. Math. Statist.,38, 1520–1535.zbMATHMathSciNetGoogle Scholar
  2. [2]
    Ghosh, M. (1969). Asymptotically optimal nonparametric tests for miscellaneous problems of linear regression, Unpublished doctoral dissertation, University of North Carolina at Chapel Hill.Google Scholar
  3. [3]
    Hájek, J. (1961). Some extensions of the Wald-Wolfowitz-Noether theorem,Ann. Math. Statist.,32, 506–523.zbMATHMathSciNetGoogle Scholar
  4. [4]
    Hájek, J. (1962). Asymptotically most powerful rank order tests,Ann. Math. Statist.,33, 1124–1147.zbMATHMathSciNetGoogle Scholar
  5. [5]
    Hájek, J. and Šidák, Z. (1967).Theory of Rank Tests, Academic Press, New York.zbMATHGoogle Scholar
  6. [6]
    Hannan, E. J. (1956). The asymptotic power of tests based on multiple correlation,J. Roy. Statist. Soc. Ser. B,18, 227–233.zbMATHMathSciNetGoogle Scholar
  7. [7]
    Loève, M. (1963).Probability Theory (Third Edition), Van Nostrand, Princeton.Google Scholar
  8. [8]
    Sen, P. K. (1967). Asymptotically most powerful rank order tests for grouped data,Ann. Math. Statist.,38, 1229–1239.zbMATHMathSciNetGoogle Scholar
  9. [9]
    Sugiura, N. (1964). A generalization of the Wilcoxon test for censored data II,Osaka J. Math.,1, 165–174.zbMATHMathSciNetGoogle Scholar
  10. [10]
    Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large,Trans. Amer. Math. Soc.,54, 426–482.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Institute of Statistical Mathematics 1973

Authors and Affiliations

  • Malay Ghosh
    • 1
    • 2
  1. 1.University of North Carolina at Chapel HillChapel HillUSA
  2. 2.Indian Statistial InstituteCulcutta

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