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

报告时间：2017年11月29日（周三） 15:30

报告地点：统计学院办公楼1层104会议室

主讲人：崔恒建，首都师范大学教授，博士生导师。曾任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杰出的研究成果，发表论文120余篇。多次赴美国、意大利、新加坡、澳大利亚和香港等著名大学进行学术合作研究。主持了国家自然科学基金杰青（B）项目和4项国家自然科学基金面上项目以及青年基金项目；主要参加了国家自然科学基金重点项目、主任基金项目、面上项目，教育部重大科研基金项目，科技部863项目，教育部留学回国人员基金，高校博士点专项基金等15余项。曾获得教育部高等学校科学技术奖-自然科学奖二等奖；全国统计科学研究优秀成果奖一等奖；京津地区五四青年概率统计“盖洛普”奖；第六届中国科协期刊优秀学术论文奖等。

报告摘要：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 andthe 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.