TESTING CONDITIONAL INDEPENDENCE USING MAXIMAL NONLINEAR CONDITIONAL CORRELATION

• 成果类型: Article
• 署名作者: Huang, Tzee-Ming
• 署名单位: National Chengchi University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS770
• 发表日期: 2010
• 页码: 2047-2091
• 关键词: association

摘要

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.