Abstract

AL-MASRI, ABEDEL-QADER  and  AL-MOMANI, NOOR. Bahadur's Stochastic Comparison of Combining infinitely Independent Tests in Case of Extreme Value Distribution. Rev.Colomb.Estad. [online]. 2022, vol.45, n.1, pp.193-208.  Epub Jan 17, 2023. ISSN 0120-1751.  https://doi.org/10.15446/rce.v45n1.97466.

For simple null hypothesis, given any non-parametric combination method which has a monotone increasing acceptance region, there exists a problem for which this method is most powerful against some alternative. Starting from this perspective and recasting each method of combining p-values as a likelihood ratio test, we present theoretical results for some of the standard combiners which provide guidance about how a powerful combiner might be chosen in practice. In this paper we consider the problem of combining n independent tests as n → ∞ for testing a simple hypothesis in case of extreme value distribution (EV(θ,1)). We study the six free-distribution combination test producers namely; Fisher, logistic, sum of p-values, inverse normal, Tippett's method and maximum of p-values. Moreover, we studying the behavior of these tests via the exact Bahadur slope. The limits of the ratios of every pair of these slopes are discussed as the parameter θ → 0 and θ → ∞. As θ → 0,, the logistic procedure is better than all other methods, followed in decreasing order by the inverse normal, the sum of p-values, Fisher, maximum of p-values and Tippett's procedure. Whereas, θ → ∞the logistic and the sum of p-values procedures are equivalent and better than all other methods, followed in decreasing order by Fisher, the inverse normal, maximum of p-values and Tippett's procedure.

Keywords : Bahadur efficiency; Bahadur slope; combining independent tests; extreme value distribution.

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