Al-Momani Marwan, Ghanim Firas, Al-Janaby Hiba Fawzi
Department of Mathematics, College of Sciences, University of Sharjah, United Arab Emirates.
Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.
Heliyon. 2024 Jul 5;10(14):e33954. doi: 10.1016/j.heliyon.2024.e33954. eCollection 2024 Jul 30.
In this paper, we compared the Exact Bahadur Slope (EBS) and the asymptotic relative efficiency of four combination methods for testing a single hypothesis against a one-sided alternative in the case of Pareto distribution when the number of tests tends to infinity. These methods combine the p-value of the corresponding test into one overall test. Fisher's, logistic, the sum of p-values, and inverse normal procedures are the four techniques used in our study. To study the performance of the combination methods, we derived the EBS expressions and compared the limit ratios locally and for large values of the shape parameter of the Pareto distribution via EBS. We also computed the EBS numerically for when the parameter of interest starts moving from the null space and applied the four methods to real data examples. We found that Fisher's method uniformly dominates the other methods in terms of EBS.
在本文中，我们比较了精确巴哈杜尔斜率（EBS）以及在帕累托分布情形下，当检验次数趋于无穷时，针对单侧备择假设检验单个假设的四种组合方法的渐近相对效率。这些方法将相应检验的p值组合成一个总体检验。我们研究中使用的四种技术是费希尔方法、逻辑斯蒂方法、p值之和方法以及逆正态方法。为了研究这些组合方法的性能，我们推导了EBS表达式，并通过EBS在局部以及对于帕累托分布形状参数的大值比较了极限比率。我们还针对感兴趣的参数开始从原假设空间移动的情况数值计算了EBS，并将这四种方法应用于实际数据示例。我们发现，就EBS而言，费希尔方法始终优于其他方法。
