Title: Two-sample modified Anderson-Darling test and its properties
Authors: Masato Kitani - Tokyo University of Science (Japan) [presenting]
Yuyan Ma - Tokyo University of Science (Japan)
Hidetoshi Murakami - Tokyo University of Science (Japan)
Abstract: Two-sample testing problem is widely used in many scientific fields. We are interested in testing whether two independent samples of distributions are equal. One of the powerful and useful conventional tests for such a situation is the two-sample Anderson-Darling test. Many researchers have discussed various improvements to the Anderson-Darling test statistic. We propose two modifications of the Anderson-Darling test statistic that emphasize the upper or lower tails of the distribution. It is necessary to derive the limiting distribution of the modified Anderson-Darling test statistic for practical analysis. Then, we prove that the limiting distribution of proposed test statistics is expressed as the weighted sum of chi-squared random variables. Additionally, we investigate the convergence to the limiting distribution and compare the powers of proposed tests with existing tests for various distributions via simulation studies. Finally, the application to real datasets demonstrates the usefulness of the proposed tests.