The Annals of Statistics

Testing conditional independence using maximal nonlinear conditional correlation

Tzee-Ming Huang

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Abstract

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.

Article information

Source
Ann. Statist., Volume 38, Number 4 (2010), 2047-2091.

Dates
First available in Project Euclid: 11 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aos/1278861242

Digital Object Identifier
doi:10.1214/09-AOS770

Mathematical Reviews number (MathSciNet)
MR2676883

Zentralblatt MATH identifier
1202.62078

Subjects
Primary: 62H20: Measures of association (correlation, canonical correlation, etc.)
Secondary: 62H15: Hypothesis testing 62G10: Hypothesis testing

Keywords
Measure of association measure of conditional association conditional independence test

Citation

Huang, Tzee-Ming. Testing conditional independence using maximal nonlinear conditional correlation. Ann. Statist. 38 (2010), no. 4, 2047--2091. doi:10.1214/09-AOS770. https://projecteuclid.org/euclid.aos/1278861242


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