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Constructing unbiased tests for homogeneity and goodness of fit

Author

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  • Cohen, Arthur
  • Sackrowitz, H. B.

Abstract

Suppose Xij, i=1, 2,..., k, j=1, 2,..., ni, are random samples from independent populations distributed according to an exponential family with parameter [theta]i. Let Yi be the minimal sufficient statistic for population i and assume that the sum of any subset of the Yi, i=1, 2,..., k, is also a one parameter exponential family. The normal and Poisson distributions satisfy such an assumption. The problem is to test H: [theta]1=[theta]2= ... =[theta]k vs K: not H. Unbiased tests are constructed. The construction ca so that the resulting unbiased tests are in a complete class in the continuous case and are admissible in the discrete case. The construction is also appropriate for testing a simple hypothesis concerned with multinomial probabilities against an arbitrary alternative. This latter problem arises in testing goodness of fit.

Suggested Citation

  • Cohen, Arthur & Sackrowitz, H. B., 1991. "Constructing unbiased tests for homogeneity and goodness of fit," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 351-355, October.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:4:p:351-355
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    Cited by:

    1. Koudou, A. E. & Pommeret, D., 2002. "A Characterization of Poisson-Gaussian Families by Convolution-Stability," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 120-127, April.

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