A General Asymptotic Framework for Distribution-Free Graph-Based Two-Sample Tests
分布无关的图型两样本检验：统一渐近框架AI 解读 ↓
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分布无关的图型两样本检验：统一渐近框架
- 研究问题
- 如何统一分析多元分布相等性的图型两样本检验，并解释底层图的组合结构怎样影响检验的渐近效率？
- 方法与思路
- 作者定义一般的分布无关图型检验，推导其 Pitman 渐近效率，将几何图检验和多元数据深度检验纳入统一框架。
- 材料陈述的贡献
- 摘要称框架涵盖近邻图、交叉匹配和广义边计数等检验，揭示图的组合性质与检验表现的联系，并提供数据示例。
- 阅读关注点
- 应核对分布无关性的含义、局部备择与图增长条件，以及各检验效率比较的适用范围和实际选用规则。
- 阅读边界
- 仅据 Crossref 摘要；未提供效率公式、具体正则条件或数据结果，不能据此认定某类图检验在所有情形下更好。
原文摘要
Summary Testing equality of two multivariate distributions is a classical problem for which many non-parametric tests have been proposed over the years. Most of the popular two-sample tests, which are asymptotically distribution free, are based either on geometric graphs constructed by using interpoint distances between the observations (multivariate generalizations of the Wald–Wolfowitz runs test) or on multivariate data depth (generalizations of the Mann–Whitney rank test). The paper introduces a general notion of distribution-free graph-based two-sample tests and provides a unified framework for analysing and comparing their asymptotic properties. The asymptotic (Pitman) efficiency of a general graph-based test is derived, which includes tests based on geometric graphs, such as the Friedman–Rafsky test, the test based on the K-nearest-neighbour graph, the cross-match test and the generalized edge count test, as well as tests based on multivariate depth functions (the Liu–Singh rank sum statistic). The results show how the combinatorial properties of the underlying graph affect the performance of the associated two-sample test and can be used to validate and decide which tests to use in practice. Applications of the results are illustrated both on synthetic and on real data sets.