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August 2010 Testing conditional independence using maximal nonlinear conditional correlation
Tzee-Ming Huang
Ann. Statist. 38(4): 2047-2091 (August 2010). DOI: 10.1214/09-AOS770


In this paper, the maximal nonlinear conditional correlation of two random vectors X and Y given another random vector Z, denoted by ρ1(X, Y|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 ∑k=1nZfZ(zk)ρ12(X, Y|Z = zk), where fZ is the probability density function of Z and the zk’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.


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Tzee-Ming Huang. "Testing conditional independence using maximal nonlinear conditional correlation." Ann. Statist. 38 (4) 2047 - 2091, August 2010.


Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1202.62078
MathSciNet: MR2676883
Digital Object Identifier: 10.1214/09-AOS770

Primary: 62H20
Secondary: 62G10, 62H15

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 4 • August 2010
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