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UI Score Tests for Some Restricted Alternatives in Exponential Families

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  • Tsai, M. T. M.

Abstract

In an exponential family of distributions, the problem of testing for homogeneity of a set of parameters against some restricted alternatives is considered. Incorporating Roy's union-intersection (UI) principle, Rao's efficient score test is extended to such restricted alternatives, and is shown to be asymptotically power-equivalent to the corresponding restricted likelihood ratio tests (for contiguous alternatives). Asymptotic null distributions of such UI score test statistics and their rates of convergence are studied. Multivariase problems for general forms of restricted alternatives are considered in the same vein. It is also shown that the UI score test is Bahadur deficiency of order O(log n).

Suggested Citation

  • Tsai, M. T. M., 1993. "UI Score Tests for Some Restricted Alternatives in Exponential Families," Journal of Multivariate Analysis, Elsevier, vol. 45(2), pages 305-323, May.
    • Handle: RePEc:eee:jmvana:v:45:y:1993:i:2:p:305-323
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    Cited by:

    1. Sen, Pranab K. & Tsai, Ming-Tien, 1999. "Two-Stage Likelihood Ratio and Union-Intersection Tests for One-Sided Alternatives Multivariate Mean with Nuisance Dispersion Matrix," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 264-282, February.

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