时间：2018年4月13日 下午2:30-3:30
地点：明德主楼1016会议室
题目：：Conditional distance correlation
摘要：Statistical inference on conditional dependence is essential in many fields including genetic association studies and graphical models. The classic measures focus on linear conditional correlations and are incapable of characterizing nonlinear conditional relationship including nonmonotonic relationship. To overcome this limitation, we introduce a nonparametric measure of conditional dependence for multivariate random variables with arbitrary dimensions. Our measure possesses the necessary and intuitive properties as a correlation index. Briefly, it is zero almost surely if and only if two multivariate random variables are conditionally independent given a third random variable. More importantly, the sample version of this measure can be expressed elegantly as the root of a V or U-process with random kernels and has desirable theoretical properties. Based on the sample version, we propose a test for conditional independence, which is proven to be more powerful than some recently developed tests through our numerical simulations. The advantage of our test is even greater when the relationship between the multivariate random variables given the third random variable cannot be expressed in a linear or monotonic function of one random variable versus the other. We also show that the sample measure is consistent and weakly convergent, and the test statistic is asymptotically normal. By applying our test in a real data analysis, we are able to identify two conditionally associated gene expressions, which otherwise cannot be revealed. Thus, our measure of conditional dependence is not only an ideal concept, but also has important practical utility.
简介：王学钦，中山大学数学学院和中山医学院双聘教授，博士生导师，中山大学华南统计科学研究中心执行主任，教育部统计专业教指委委员。王学钦教授2003年获得美国纽约州立大学宾厄姆敦分校博士学位，2007年入职中山大学任教授，2012年入选中山大学首届优秀青年教师培养计划、教育部新世纪优秀人才支持计划，2013年获得国家自然科学基金优秀青年基金，2014年被评为第八批广东省高等学校“千百十工程”国家级培养对象，2016年入选“广东特支计划”百千万工程领军人才。其研究领域包括非参多元统计学、统计学习、精准医学等。