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On a stochastic inequality for the wilks statistic

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An Erratum to this article was published on 01 December 1976

Summary

The general nonnull distribution of Wilks statistic, the likelihood ratio statistic in MANOVA, can be expressed as a product of conditional beta variables [3]. Making use of this results, in the present paper, an upper bound for the nonnull distribution of Wilks statistic is obtained, which provides a conservative evaluation of the power of the likelihood ratio test for the cases when the alternative hypothesis is of rank 1, 2 or 3. Forp=2, wherep is the number of variables, and largef 2, the degrees of freedom, it has been shown that the results of this paper give a much better approximation to the power of Wilks statistic than Mikhail's approximation [10]. A few percentage points have also been computed forp=3 and selected values of the degrees of freedom and the noncentrality parameters, which in the linear case have been compared with the exact values obtained by the author [7].

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Authors and Affiliations

  1. University of Michigan, Michigan, USA

    A. K. Gupta

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  1. A. K. Gupta
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Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/BF02504735.

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Gupta, A.K. On a stochastic inequality for the wilks statistic. Ann Inst Stat Math 27, 341–348 (1975). https://doi.org/10.1007/BF02504653

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  • DOI: https://doi.org/10.1007/BF02504653

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