Exact Bahadur Slope for Combining Independent Tests in the Case of the Pareto Distribution

In this paper, we compared the Exact Bahaudr Slope (EBS) and the asymptotic relative efficiency of four combination methods for testing asingle hypothesis against a one-sided alternative in the case of Pareto distribution when the number of tests tends to infinity. These methods combinethe 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 techniquesused 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 numerically the EBS for when the parameter of interest starts moving from the null space. We found that the Fisher’s method uniformly dominates the other methods in terms of EBS