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Bahadur’s Stochastic Comparison of Combining infinitely Independent Tests in Case of Extreme Value Distribution
Comparación estocástica de Bahadur de la combinación de pruebas infinitamente independientes en caso de distribución de valor extremo
DOI:
https://doi.org/10.15446/rce.v45n1.97466Keywords:
Extreme value distribution, Bahadur efficiency, Bahadur slope, Combining independent tests (en)Combinación de pruebas independientes, Distribución de valor extremo, Eficiencia Bahadur, Pendiente Bahadur (es)
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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 pvalues 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.
Para hipótesis nulas simples, dado cualquier método de combinación no paramétrico que tenga una región de aceptación creciente monótona, existe un problema para el cual este método es más poderoso frente a alguna alternativa. Partiendo de esta perspectiva y reformulando cada método de combinación de valores p como una prueba de razón de verosimilitud, presentamos resultados teóricos para algunos de los combinadores estándar que brindan orientación sobre cómo se podría elegir un combinador poderoso en la práctica. En este artículo consideramos el problema de combinar pruebas independientes de n como n → ∞ para probar una hipótesis simple en el caso de una distribución de valor extremo (EV (θ, 1)). Estudiamos los seis productores de prueba de combinación de distribución gratuita, a saber; Fisher, logística, suma de valores p, normal inversa, método de Tippett y máximo de valores p. Además, estudiamos el comportamiento de estas pruebas a través de la pendiente exacta de Bahadur. Los límites de las razones de cada par de estas pendientes se analizan como el parámetro θ → 0 y θ → ∞. Como θ → 0, la logística El procedimiento es mejor que todos los
demás métodos, seguido en orden decreciente por el inverso normal, la suma de valores p, Fisher, el máximo de valores p y el procedimiento de Tippett. Considerando que, θ → ∞ la logística y la suma de los procedimientos de valores p so equivalentes y mejores que todos los demás métodos, seguidos en orden decreciente por Fisher, la inversa normal, máxima de valores p y procedimiento de Tippett.
References
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1. Marwan Al-Momani, Firas Ghanim, Hiba Fawzi Al-Janaby. (2024). Exact Bahadur Slope for combining independent tests in the case of the Pareto distribution. Heliyon, 10(14), p.e33954. https://doi.org/10.1016/j.heliyon.2024.e33954.
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