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. (Joint work with Leheng Cai and Xu Guo)

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。