BET on Independence
BET：基于二进制展开的独立性检验AI 解读 ↓
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BET：基于二进制展开的独立性检验
- 研究问题
- 非参数独立性检验如何避免非一致相合性造成的严重功效损失，并在拒绝独立性后提供可解释的总体依赖关系？
- 方法与思路
- 作者以 copula 的二进制展开滤过近似构造 BEStat 与 BET，通过 Hadamard 变换得到对称统计量，并支持位运算实现。
- 材料陈述的贡献
- 摘要称，对称统计量对依赖具有完全充分性且在零假设下不相关；BET 达到可靠功效所需样本量的极小极大速率并提供解释。
- 阅读关注点
- 应核对滤过分辨率、备择集合、完全充分性的适用对象及速率条件，查明功效比较设置和拒绝后关系解释的具体构造。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；摘要未说明完整检验条件、分辨率选择和比较数值，不能认定其对所有依赖形式占优。
原文摘要
Kai Zhang* Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NCCONTACT Kai Zhang zhangk@email.unc.edu Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599.* This article is dedicated to Professor Lawrence D. Brown with the author’s deepest appreciation for his teaching and mentoring.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.AbstractWe study the problem of nonparametric dependence detection. Many existing methods may suffer severe power loss due to nonuniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test of independence through the new framework of binary expansion statistics (BEStat) and binary expansion testing (BET), which examine dependence through a novel binary expansion filtration approximation of the copula. Through a Hadamard transform, we find that the symmetry statistics in the filtration are complete sufficient statistics for dependence. These statistics are also uncorrelated under the null. By using symmetry statistics, the BET avoids the problem of nonuniform consistency and improves upon a wide class of commonly used methods (a) by achieving the minimax rate in sample size requirement for reliable power and (b) by providing clear interpretations of global relationships upon rejection of independence. The binary expansion approach also connects the symmetry statistics with the current computing system to facilitate efficient bitwise implementation. We illustrate the BET with a study of the distribution of stars in the night sky and with an exploratory data analysis of the TCGA breast cancer data. Supplementary materials for this article are available online.