A robust combination test for goodness-of-fit

Goodness-of-fit testing is a fundamental problem in statistics and has attracted considerable attention from researchers. However, in recent years, most newly proposed tests have been tailored to specific distributions, with relatively few general-purpose goodness-of-fit tests available. This highlights the need for a versatile test applicable to a broad range of distributions. In this paper, we first introduce a series of statistics for testing goodness-of-fit based on empirical distribution function (EDF), and establish the asymptotic distribution of each EDF statistic. The proposed final test statistic is constructed as the weighted sum of transformed p-values derived from each EDF statistic, which approximately follows standard Cauchy distribution. Extensive simulation studies demonstrate that the proposed method is efficiency-robust, in the sense of maintaining high power under small data contamination, and outperforms other existing methods under a wide range of alternative distributions. We further illustrate the performance of our test on several real datasets.