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.

翻译：在本篇文章中,我们引入了一种新的差异,称为最大差异差异,以衡量Hilbert空格中两个分布之间的差异,而这两个分布通过最大平均值差异是无法找到的。我们还建议基于这一差异进行两个样板的合适测试。我们获得了这个两个样板测试的无药可救的无效分布,为测试无效分布提供了有效的近似法。