Two Sample Testing in High Dimension via Maximum Mean Discrepancy

Understand

Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space.

• The asymptotic property of the sample MMD has been well studied when the dimension $p$ is fixed using the theory of U-statistic.
• As motivated by the frequent use of MMD test for data of moderate/high dimension, we propose to investigate the behavior of the sample MMD in a high-dimensional environment and develop a new studentized test statistic.
• Specifically, we obtain the central limit theorems for the studentized sample MMD as both the dimension $p$ and sample sizes $n,m$ diverge to infinity.