报告题目：Testing for conditional independence: a groupwise dimension reduction-based adaptive-to-model approach

报告人：朱学虎 副教授

报告摘要: In this paper, we propose an adaptive-to-model test for conditional independence through groupwise dimension reduction developed in sufficient dimension reduction field. The test statistic under the null hypothesis is asymptotically normally distributed. Although it is also based on nonparametric estimation like any local smoothing tests for conditional independence, its behavior is similar to existing local smoothing tests with only the number of covariates under the null hypothesis. Further, it can detect local alternatives distinct from the null at the rate that is also only related to the number of covariates under the null hypothesis. Therefore, the curse of dimensionality is largely alleviated. To achieve the above goal, we also suggest a groupwise least squares estimation for the groupwise central subspace in sufficient dimension reduction. It is of its own importance in estimation theory though it is as a by-product for the model adaptation of test statistic described herewith. Numerical studies and analyses for two real data sets are then conducted to examine the finite sample performance of the proposed test.

报告时间：12月11日上午9:00-10:00

报告地点：腾讯会议ID号：724 744 632

主办单位：我院

报告人简介：朱学虎，博士，西安交通大学副教授，硕士生导师，于2015年在香港浸会大学和山东大学获得双博士学位，2017.01–2017.06在香港浸会大学做王宽城教育基金高级访问学者，2016.01进入西安交通大学数学与我院工作。目前主要从事高维数据分析、统计学习、充分降维、拟合优度检验等领域的基础理论与应用研究。其研究成果在Statistics and Computing, Scandinavian Journal of Statistics, Statistica Sinica, IEEE Transactions on Geoscience and Remote Sensing， Computational Statistics & Data Analysis，Journal of Multivariate Analysis等期刊上发表SCI或SSCI学术论文20余篇。先后主持国家自然科学青年基金、博士后特别资助项目，作为研究骨干成员参与科技部重大项目和国家自然科学基金面上项目。