TESTING CONDITIONAL INDEPENDENCE USING MAXIMAL NONLINEAR CONDITIONAL CORRELATION
TESTING CONDITIONAL INDEPENDENCE USING MAXIMAL NONLINEAR CONDITIONAL CORRELATION
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DOI：
10.1214/09-aos770
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发表时间：
2010-08-01
影响因子：
4.5
通讯作者：
Huang, Tzee-Ming
中科院分区：
文献类型：
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作者：
Huang, Tzee-Ming
本文给出了两个随机向量X和Y在给定另一个随机向量Z的情况下的最大非线性条件相关。表示为rho（1）（X. Y竖线Z）被定义为满足某些期望性质的条件关联的度量。当Z是连续的时，用于检验给定Z的X和Y的条件独立性的检验基于Sigma（nZ）（k=1）f（Z）（z（k））rho（2）（1）（X，Y竖线Z = z（k））形式的加权平均的估计量来构造。其中f（Z）是Z的概率密度函数，z（k）是Z范围内的一些点。在一定的条件下，证明了检验统计量在条件独立下是渐近正态的，且检验是相合的。
In this paper, the maximal nonlinear conditional correlation of two random vectors X and Y given another random vector Z. denoted by rho(1) (X. Y vertical bar Z), is defined as a measure of conditional association, which satisfies certain desirable properties. When Z is continuous, a test for testing the conditional independence of X and Y given Z is constructed based on the estimator of a weighted average of the form Sigma(nZ)(k=1) f(Z)(z(k))rho(2)(1) (X, Y vertical bar Z = z(k)). where f(Z) is the probability density function of Z and the z(k)'s are some points in the range of Z. Under some conditions, it is shown that the test statistic is asymptotically normal under conditional independence, and the test is consistent.