报告题目：Dimensionality determination in dimension reduction: a thresholding double ridge ratio approach

报告人: 朱学虎，西安交通大学，副教授，硕士生导师

报告时间：2019年12月24号(周二)  上午 9:00-12:00

报告地点： 数学馆310会议室

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。目前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。在Statistics and Computing, Statistica Sinica, IEEE Transactions on Geoscience and Remote Sensing， Computational Statistics & Data Analysis，Journal of Multivariate Analysis等国际知名期刊上发表学术论文多篇。先后主持国家自然科学青年基金、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。

报告摘要：Underdetermination of model dimensionality (order) is a longstanding problem when existing eigendecomposition-based criteria are used. To alleviate this difficulty, we propose a thresholding double ridge ratio criterion in this paper. Unlike all existing eigendecomposition-based criteria, the proposed criterion can provide a consistent estimate even when there are several local minima. For illustration, we present the generic strategy with three important applications: dimension reduction in regressions with fixed and divergent dimensions; model checking with local alternative models; and ultra-high dimensional approximate factor models. Numerical studies are conducted to examine the finite sample performance of the proposed method and a real data example is analysed for illustration.