A1929
Title: A framework for multivariate goodness-of-fit testing based on matrix distances
Authors: Marianthi Markatou - University at Buffalo (United States) [presenting]
Abstract: Measures of discrepancy between two probability distributions are used in scientific literature to develop goodness-of-fit methods. A unified framework for the study of two-sample and k-sample goodness-of-fit testing based on the concept of matrix distance is presented. The matrix distance is first defined, and its elements are then used to construct test statistics for testing equality in distribution of k-samples. The two-sample test statistic is shown to be a special case of the k-sample test statistic. The asymptotic distributions of the tests under the null hypothesis are derived, and the connection of the MMD statistic with the proposed tests is illustrated. Computational considerations are presented, and the implementation of these methods is demonstrated via the QuadratiK software. Simulation results exemplify the performance of the new methods and compare it with that of state-of-the-art procedures.
