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

主讲人：朱学虎  西安交通大学

讲座时间：2019年12月23日（周一）上午10：00—11：00

讲座地点：综合楼601

主讲人简介：

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统计学院工作。主要从事高维数据分析、充分降维、拟合优度检验等领域的研究。其研究成果在Statistics and Computing, Statistica Sinica, IEEE Transactions on Geoscience and Remote Sensing， Computational Statistics & Data Analysis，Journal of Multivariate Analysis等国际知名期刊。先后主持国家自然科学基金、博士后特别资助、博士后面上项目，作为骨干成员参加国家科技部重大项目一项，国家自然科学基金面上项目4项。

讲座摘要：

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 behaviour 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. Numerical studies and two real data analyses are then conducted to examine the finite sample performance of the proposed test.