報 告 人： 楊艷榮 博士
報告題目：Can we trust PCA on non-stationary data?
楊艷榮，澳大利亞國立大學高級講師，畢業於新加坡南洋理工大學，主要研究方向為高維統計推斷、隨機矩陣理論、函數型數據分析等，在Annal of Statistics, JRSSB, JASA等統計學頂級期刊發表多篇學術論文。
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.