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A linear approximation to the power function of a test

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  • A. García-Pérez

Abstract

In this paper we obtain a linear approximation to the power function of a test that is very accurate for small sample sizes. This is especially useful for robust tests where not many power functions are available. The approximation is based on the von Mises expansion of the tail probability functional and on the Tail Area Influence Function (TAIF). The goals of the paper are, first to extend the definition of the TAIF to the case of non identically distributed random variables, defining the Partial Tail Area Influence Functions and the Vectorial Tail Area Influence Function; second, to obtain exact expressions for computing these new influence functions; and, finally, to find accurate approximations to the power function, that can be used in the case of non identically distributed random variables. We include some examples of the application of this linear approximation to tests that involve the Huber statistic and also saddlepoint tests, so proving that the approximations apply not only to simple problems but also to complex ones. Copyright Springer-Verlag 2012

Suggested Citation

  • A. García-Pérez, 2012. "A linear approximation to the power function of a test," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 855-875, October.
    • Handle: RePEc:spr:metrik:v:75:y:2012:i:7:p:855-875
    DOI: 10.1007/s00184-011-0356-6
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    References listed on IDEAS

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    1. Lô, Serigne N. & Ronchetti, Elvezio, 2009. "Robust and accurate inference for generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2126-2136, October.
    2. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
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    Cited by:

    1. Stephanie Aerts & Gentiane Haesbroeck, 2017. "Robust asymptotic tests for the equality of multivariate coefficients of variation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 163-187, March.

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