时间：2018年11月21日(周三)下午16:00-17:00
地点：闵行校区法商南楼302室
题目：Hypothesis testing on linear structures of high dimensional covariance matrix
主讲人：陈钊研究员 复旦大学大数据学院
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. We illustrate the proposed testing procedure by an empirical analysis of Chinese stock market data.
报告人介绍：
陈钊，复旦大学大数据学院青年研究员，2012年在中国科学技术大学获得博士学位。之后在美国普林斯顿大学，宾夕法尼亚州立大学从事博士后研究及研究型助理教授工作。主要研究方向包括高维统计推断，稳健回归，时间序列，非参数及半参数统计方法，以及将统计方法应用于建筑能源，生物信息，癌症研究等领域。科研成果发表在AoS, JASA, Statistica Sinica, Energy and buildings等期刊上。