Two-sample test based on maximum variance discrepancy

TL;DR

This paper introduces the maximum variance discrepancy, a new measure for comparing distributions in Hilbert spaces, and develops a two-sample test with an efficient asymptotic null distribution approximation.

Contribution

The paper proposes a novel discrepancy measure, maximum variance discrepancy, and a corresponding two-sample test that improves upon existing methods in Hilbert space distribution comparison.

Findings

The maximum variance discrepancy effectively captures differences between distributions.

The two-sample test based on this discrepancy has an analytically derived asymptotic null distribution.

The method provides an efficient approximation for the null distribution in practice.

Abstract

In this article, we introduce a novel discrepancy called the maximum variance discrepancy for the purpose of measuring the difference between two distributions in Hilbert spaces that cannot be found via the maximum mean discrepancy. We also propose a two-sample goodness of fit test based on this discrepancy. We obtain the asymptotic null distribution of this two-sample test, which provides an efficient approximation method for the null distribution of the test.