报告人：郑术蓉(东北师范大学)

报告题目：Hypothesis Testing on Linear Structures of High Dimensional Covariance Matrix

报告摘要：This paper is concerned with test of significance on high dimensional covariance structures, and aims to develop a unified framework for testing commonly-used linear covariance structures. We first construct a consistent estimator for parameters involved in the linear covariance structure, and then develop two tests for the linear covariance structures based on entropy loss and quadratic loss used for covariance matrix estimation. To study the asymptotic properties of the proposed tests, we study related high dimensional random matrix theory, and establish several highly useful asymptotic results. With the aid of these asymptotic results, we derive the limiting distributions of these two tests under the null and alternative hypotheses. We further show that the quadratic loss based test is asymptotically unbiased. We conduct Monte Carlo simulation study to examine the finite sample performance of the two tests. Our simulation results show that the limiting null distributions approximate their null distributions quite well, and the corresponding asymptotic critical values keep Type I error rate very well. Our numerical comparison implies that the proposed tests outperform existing ones in terms of controlling Type I error rate and power. Our simulation indicates that the test based on quadratic loss  seems to have better power than the test based on entropy loss.

报告人简介：郑术蓉，现为东北师范大学sunbet中国官网 教授，主要从事高维数据分析、大维随机矩阵、不对称系数的研究。曾完成国家自然科学基金面上项目、青年项目各1项，现正主持国家自然科学基金优秀青年基金1项。在Journal of American Statistical Association、Annals of Statistics、Biometrika、Bioinformatics等期刊上发表和被接受发表的学术论文28篇，其中SCI期刊检索文章26篇。出版图书章节两章。在高等教育出版社以及Cambridge University Press合作出版中、英文著作各一部。博士论文《线性不等式约束下的EM算法》曾分别获得“2006年吉林省优秀博士论文”和“2006年全国优秀博士论文提名”。

报告时间： 2018年10月24日（星期三）上午10：00- 11：00.

报告地点：科技楼南楼702