The Annals of Statistics
- Ann. Statist.
- Volume 38, Number 4 (2010), 2047-2091.
Testing conditional independence using maximal nonlinear conditional correlation
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.
Ann. Statist., Volume 38, Number 4 (2010), 2047-2091.
First available in Project Euclid: 11 July 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H20: Measures of association (correlation, canonical correlation, etc.)
Secondary: 62H15: Hypothesis testing 62G10: Hypothesis testing
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