Academic

With developing data collection techniques, the analysis of complicated data objects in some separable metric spaces is an active research area. However, the theoretical results of maximum mean discrepancy (MMD)-based tests in the literature are based on a restrictive equal sample size assumption. Therefore, a further analysis on these MMD-based tests for two-sample equal-distribution testing problems with this assumption removed is needed. Further, MMD-based tests were not extended for multi-sample equal-distribution testing problems although they are needed to check if several populations have the same distribution. In this thesis, we further study MMD-based tests with the equal sample size assumption removed and extend them for multi-sample equal-distribution testing problems. We also establish the asymptotic null and alternative distributions of the test statistics, and several approaches for approximating their null distributions. Simulation studies and real data applications demonstrate the good performance of the proposed tests against some existing tests.