BET on Independence
BET on Independence
复制标题
DOI：
10.1080/01621459.2018.1537921
复制
发表时间：
2019-04-23
影响因子：
3.7
通讯作者：
Zhang, Kai
中科院分区：
文献类型：
--
作者：
Zhang, Kai
我们研究非参数依赖性检测问题。许多现有的方法可能会由于不一致的一致性而遭受严重的功率损失，我们用一个悖论来说明这一点。为了避免这种功率损失，我们通过二元展开统计（BEStat）和二元展开测试（BET）的新框架来进行独立性的非参数测试，通过新的二元展开过滤近似来检查依赖性。通过哈达玛变换，我们发现过滤中的对称统计量是完全足够的依赖统计量。这些统计数据在零值下也是不相关的。通过使用对称统计，BET 避免了不一致一致性问题，并改进了多种常用方法（a）通过实现可靠功效的样本量要求的极小最大率，以及（b）在拒绝独立性时提供对全局关系的清晰解释。二进制展开方法还将对称统计量与当前计算系统连接起来，以促进高效的按位实现。我们通过研究夜空中星星的分布以及对 TCGA 乳腺癌数据的探索性数据分析来说明 BET。本文可在线获取。
We 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. for this article are available online.