报告题目: A Distribution-Free Test of Independence Based on Mean Variance Index

报告人：崔恒建 教授 (首都师范大学)

主办：统计学院

时间：2017年6月11日下午15:00-16:00

地点：科技楼二楼北会议室

Abstract:  This work is concerned with testing the independence between a categorical random variable Y and a continuous one X based on mean variance index. The mean variance index can be considered as the weighted average of Cramer-von Mises distances between the conditional distribution functions of X given each class of Y and the unconditional distribution function of X. The mean variance index is zero if and only if X and Y are independent. We propose a new mean variance test based on the mean variance index between X and Y and it enjoys several appealing merits. First, under the independence between X and Y, we derive an explicit form of the asymptotic null distribution. It provides us an efficient and fast way to compute the empirical p-value in practice. Second, no assumption on the distribution of two random variables is required and the new test statistic is invariant under one-to-one transformations of the continuous random variable. Thus, the proposed test is distribution-free. Furthermore, this test is resistent to heavy-tailed distributions and extreme values in the data. In addition, the mean variance test is also applicable to test the independence between two continuous random variables by discretizing one variable. Monte Carlo simulations show that the new test has an outstanding finite-sample power performance even the continuous variable X is generated from a standard Cauchy distribution.

崔恒建教授简介：首都师范大学教授，博士生导师，为国务院学位委员会学科评议组专家。在数理统计和稳健统计理论和方法、金融统计、遥感统计与质量管理等领域取得过许多骄人和杰出的研究成果，发表论文100余篇，其中包括发表在国际顶级的统计和计量经济学杂志《Annals of Statistics》《Journal of Econometrics》《Journal of the Royal Statistical Society B》和《Biometrika》上，主持或主研基金项目共计15项。崔恒建教授现任《应用数学学报》中、英文版编委、《数理统计与管理》编委、中国概率统计学会常务理事、中国现场统计学会理事，生存分析分会理事、国际泛华统计协会会员、美国数学会数学评论员、国际数理统计学会（中国分会）常务理事。曾获第六届中国科协期刊优秀学术论文三等奖（2009）、教育部高等学校科学技术奖--自然科学奖二等奖（2006）、第八届全国统计科学研究优秀成果奖一等奖（2006）、第八届全国统计科学研究优秀教学成果奖二等奖（2006）、北京师范大学优秀科研成果奖（2002）、国家统计局全国统计科学技术进步二等奖（1998）、京津五四青年概率统计学术年会“盖洛普”奖（1997）。