The Statistics Seminar Speaker for Wednesday, February 3, 2016 is Weichen Wang, a fifth-year student in the Department of Operations Research and Financial Engineering at Princeton University. He is in the Statistics and Econometrics Lab of Prof Jianqing Fan. Before his PhD, he received his Bachelor's degree from Tsinghua University in 2011, majoring in Math and Physics. His research interests include econometrics factor analysis, high-dimensional statistical inference, random matrix theories, robust statistics, bioinformatics and modeling for massive datasets and networks.
Title: Semiparametric Factors Models and Projected Principal Component Analysis
Abstract: Factor analysis is one of the most useful tools for modeling common dependence among multivariate outputs. We propose a flexible semiparametric factor model, which decomposes the factor loading matrix into the component that can be explained by subject-specific covariates and the orthogonal residual component. The method Projected Principal Component Analysis was introduced to recover the latent structure. We show that the unobserved factors and the smooth factor loading matrices can be more accurately estimated than the conventional PCA if the projection is genuine. The convergence is achieved even when the sample size is finite. This leads us to develop nonparametric tests on whether observed covariates have explaining powers on the loadings. The proposed method is illustrated by both simulated data and the returns of the S&P 500 constituents.
Furthermore, as one application of the semiparametric model, we consider the problem of heterogeneity adjustment when aggregating datasets from multiple sources. We propose a generic framework named ALPHA (Adaptive Low-rank Principal Heterogeneity Adjustment) to model, estimate, and adjust heterogeneity from the original data. As an illustrative application of this generic framework, we conduct graphical model inference for a brain imaging network based on multiple datasets.
Refreshments will be served after the seminar in 1181 Comstock Hall.