报告题目：Model-Free Test and Measure for Partial Mean Dependence

报告时间：2023年5月19日 周五15:30-17：30

报告地点: 数理楼138

报告人：钟威教授(厦门大学王亚南经济研究院、经济学院统计学与数据科学系教授)

摘要： It is of importance to investigate the significance of a subset of covariates W for the response Y given covariates Z in regression modeling. To this end, we propose a significance test for partial mean independence based on deep neural networks and data splitting. The test statistic converges to the standard chi-squared distribution under the null hypothesis while it converges to a normal distribution under the alternative hypothesis. We suggest a powerful ensemble algorithm based on multiple data splitting to enhance the testing power. If the null hypothesis is rejected, we propose a partial Generalized Measure of Correlation (pGMC) to measure the partial mean dependence of Y given W after controlling for the nonlinear effect of Z. We present the theoretical properties of the pGMC and establish the asymptotic normality of its estimator with the optimal root-N converge rate. Furthermore, the valid confidence interval for the pGMC is also derived. As an important special case when there is no conditional covariates Z, we consider a new test of overall significance of covariates for the response in a model-free setting. Numerical studies and real data analysis are conducted to compare with existing approaches and to illustrate the validity of our procedures.

报告人简介：钟威，现任厦门大学王亚南经济研究院、经济学院统计学与数据科学系教授、系主任、博士生导师。2012年获得美国宾夕法尼亚州立大学统计学博士学位，2019年获得国家自科优青项目，2022年获得霍英东教育基金会全国高等院校青年科学奖二等奖。主要从事高维数据统计分析、统计学习算法、计量经济学、统计学和数据科学的应用等研究，在The Annals of Statistics, Journal of the American Statistical Association, Biometrika, Journal of Econometrics, Journal of Business & Economic Statistics, Biometrics, Annals of Applied Statistics,  Statistica Sinica，中国科学数学等国内外统计学权威期刊发表（含接收）30余篇论文。教学方面，曾获厦门大学第五届英语教学比赛一等奖、厦门大学第十五届青年教师技能比赛特等奖、厦门大学教学创新大赛一等奖等。