A0341
Title: Two-sample test based on the variance of a positive definite kernel
Authors: Natsumi Makigusa - Chuo University (Japan) [presenting]
Abstract: The aim is to test whether the distributions $P$ and $Q$ followed by two samples are the same. Especially a two-sample test based on Maximum Mean Discrepancy (MMD) is known as an approach for high-dimensional low-sample size data. The MMD embeds a probability distribution into the reproducing kernel Hilbert space by the mean of the positive definite kernel and measures the difference between the two distributions $P$ and $Q$ based on the distance between each embedding. We introduce a novel discrepancy called the Maximum Variance Discrepancy (MVD) for the purpose of measuring the difference between two distributions in Hilbert spaces that cannot be found via the MMD. The MVD measures the difference between the distributions $P$ and $Q$ by embedding the variances of the definite positive kernel under the $P$ and $Q$ into the tensor product space of the reproducing kernel Hilbert space and measuring these differences. We propose a two-sample test based on this MVD and obtain the asymptotic distributions of this test statistic. The asymptotic null distribution of this test statistic is the infinite sum of the weighted chi-square distribution. We propose an approximation of the null distribution to obtain the critical value.
