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Comparison of tests in the multiparameter case II. A third-order optimality property of Rao's test

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  • Mukerjee, Rahul

Abstract

In a general multiparameter setup, this paper proves an optimality property of Rao's test, in terms of maximization of "average" third-order power under contiguous alternatives, within a very wide class of tests that includes the likelihood ratio and Wald's tests. The use of a new kind of polynomials, analogous to Hermite polynomials, is helpful in the derivation of the results.

Suggested Citation

  • Mukerjee, Rahul, 1990. "Comparison of tests in the multiparameter case II. A third-order optimality property of Rao's test," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 31-48, April.
    • Handle: RePEc:eee:jmvana:v:33:y:1990:i:1:p:31-48
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    Cited by:

    1. Ferrari, Silvia L. P. & Cordeiro, Gauss M. & Uribe-Opazo, Miguel A. & Cribari-Neto, Francisco, 1996. "Improved score tests for one-parameter exponential family models," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 61-71, September.
    2. Kakizawa, Yoshihide, 2016. "Some integrals involving multivariate Hermite polynomials: Application to evaluating higher-order local powers," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 162-168.
    3. Marc Aerts & Gerda Claeskens, 1999. "Bootstrapping Pseudolikelihood Models for Clustered Binary Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 515-530, September.

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