【主 题】 Spiked Eigenvalues of High-Dimensional Separable Sample Covariance Matrices

【报告人】 杨艳荣, 高级讲师

Australian National University

【时 间】 2019年12月17日   16:00-17:00

【地 点】 上海财经大学统计与管理学院大楼1208会议室

【摘 要】This paper establishes asymptotic properties for spiked empirical eigenvalues for high dimensional data with both cross-sectional dependence and dependent sample structure. A new finding from the established theoretical results is that spiked empirical eigenvalues will reflect dependent sample structure instead of cross-sectional structure under some scenarios, which indicates that principal component analysis (PCA) may provide inaccurate inference for cross-sectional structure. An illustrated example is provided to show that some commonly used statistics based on spiked empirical eigenvalues mis-estimate the true number of common factors. As an application on high dimensional time series, we propose a test statistic to distinguish unit root from factor structure, and demonstrate its effective finite sample performance on simulated data. Our results are then applied to analyse OECD health care expenditure data and US mortality data, both of which possess cross-sectional dependence as well as nonstationary temporal dependence. It is worth mentioning that we contribute to statistical justification for the benchmark paper by Lee and Carter (1994, JASA) in mortality forecasting.

【嘉宾简介】杨艳荣博士，澳国立大学高级讲师，毕业于新加坡南洋理工大学。杨博士的主要研究方向为高维统计推断、随机矩阵理论、函数型数据分析等，她在Annals of Statistics, Journal of the Royal Statistical Society: Series B, Journal of the American Statistical Association等统计学顶级期刊发表多篇学术论文。

【主持人】夏宁宁