报 告 人： 杨艳荣 博士
报告题目：Can we trust PCA on non-stationary data?
杨艳荣，澳大利亚国立大学高级讲师，毕♀业于新加坡南洋理工大学，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，在Annal of Statistics, JRSSB, JASA等统计学顶级期刊发表多篇学术论文。
This paper establishes asymptotic properties for spiked empirical eigenvalues for high-dimensional data with both cross-sectional dependence and a dependent sample structure. A new finding from the established theoretical results is that spiked empirical eigenvalues will reflect the dependent sample structure instead of the cross-sectional structure under some scenarios, which indicates that principal component analysis (PCA) may provide inaccurate inference for cross-sectional structures. An illustrated example is provided to show that some commonly used statistics based on spiked empirical eigenvalues misestimate the true number of common factors. As an application of high-dimensional time series, we propose a test statistic to distinguish the unit root from the factor structure and demonstrate its effective finite sample performance on simulated data. Our results are then applied to analyze OECD healthcare expenditure data and U.S. mortality data, both of which possess cross-sectional dependence as well as non-stationary temporal dependence. It is worth mentioning that we contribute to statistical justification for the benchmark paper by Lee and Carter (1992, JASA) in mortality forecasting.