Nonparametric independence testing via mutual information
Nonparametric independence testing via mutual information
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DOI：
10.1093/biomet/asz024
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发表时间：
2019-09-01
期刊：
影响因子：
2.7
通讯作者：
Samworth, R. J.
中科院分区：
文献类型：
--
作者：
Berrett, T. B.;Samworth, R. J.
我们提出了两个多元随机向量的独立性检验，给出了一个样本从潜在的人口。我们的方法是基于互信息的估计，其分解为联合熵和边际熵，便于使用最近开发的从最近邻距离导出的有效熵估计器。所建议的临界值可以在有一个近似的边缘的情况下通过模拟得到，或者通过以其他方式排列数据得到。这有利于尺寸保证，并且我们提供了局部幂分析，统一地在互信息满足下界的密度类上。我们的想法可以扩展到基于评估协变量向量的独立性和适当定义的误差向量的概念，为正态线性模型提供新的拟合优良度检验。该理论得到了模拟数据和实际数据的数值研究的支持。
We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values may be obtained by simulation in the case where an approximation to one marginal is available or by permuting the data otherwise. This facilitates size guarantees, and we provide local power analyses, uniformly over classes of densities whose mutual information satisfies a lower bound. Our ideas may be extended to provide new goodness-of-fit tests for normal linear models based on assessing the independence of our vector of covariates and an appropriately defined notion of an error vector. The theory is supported by numerical studies on both simulated and real data.