论文标题
用于分析基于内核测试的一般框架
A general framework for the analysis of kernel-based tests
论文作者
论文摘要
基于内核的测试提供了一个简单而有效的框架，该框架使用繁殖Hilbert空间的理论设计非参数测试程序。在本文中，我们提出了新的理论工具，可用于在几种数据方案以及许多不同的测试问题中研究基于内核测试的渐近行为。与当前的方法不同，我们的方法避免使用冗长的$ u $和$ v $统计信息扩展并限制定理，该定理通常出现在文献中，并直接与希尔伯特（Hilbert）空格上的随机功能合作。因此，我们的框架会导致对内核测试的简单明了的分析，只需要轻度的规律性条件。此外，我们表明，总的来说，不能通过证明我们方法所需的规律性条件既足够又足够必要来改进我们的分析。为了说明我们的方法的有效性，我们为有条件的独立性测试问题提供了一项新的内核测试，以及针对已知的基于内核测试的新分析。
Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the asymptotic behaviour of kernel-based tests in several data scenarios, and in many different testing problems. Unlike current approaches, our methods avoid using lengthy $U$ and $V$ statistics expansions and limit theorems, that commonly appear in the literature, and works directly with random functionals on Hilbert spaces. Therefore, our framework leads to a much simpler and clean analysis of kernel tests, only requiring mild regularity conditions. Furthermore, we show that, in general, our analysis cannot be improved by proving that the regularity conditions required by our methods are both sufficient and necessary. To illustrate the effectiveness of our approach we present a new kernel-test for the conditional independence testing problem, as well as new analyses for already known kernel-based tests.
