Theory of Functional PCA for noisy and discretely observed data

Title: Theory of  Functional PCA for noisy and discretely observed data

Speaker: Yao Fang (Peking University)

Time: 2023-03-24, 15:00

Location: Tecent Meeting Room 545-515-268

Abstract:  Functional data analysis is an important research field in statistics which treats  data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) plays a central role for data reduction and representation. After nearly three decades of research, there remains a key problem unsolved, namely,  the perturbation analysis of covariance operator for diverging number of eigencomponents obtained from noisy and discretely observed data. This is fundamental for studying models and methods based on FPCA, while there has not been much progress since the result obtained by Hall et al.(2006) for a fixed number of eigenfunction estimates. In this work, we establish a unified theory for this problem, deriving the moment bounds of eigenfunctions and asymptotic distributions of eigenvalues for a wide range of sampling schemes. We also exploit double truncation to derive the uniform convergence of such estimated eigenfunctions. The technical arguments in this work are useful for handling the perturbation series of discretely observed functional data and can be applied in models and methods involving inverse using FPCA as regularization, such as functional linear regression.

Introduction of the speaker: Dr. Fang Yao is Chair Professor in Statistics at Peking University (PKU), serving as the Department Head of Probability & Statistics and the Director of the Center for Statistical Science at PKU. He is a Fellow of the Institute of Mathematical Statistics (IMS), the American Statistical Association (ASA), and an elected member of International Statistical Institute (ISI). Dr. Yao received his B.S. degree in 2000 from University of Science & Technology in China, and his Ph.D. degree in Statistics in 2003 at University of California, Davis under the supervision of Prof. Hans G. Müller and Jane-Ling Wang. He was a tenured Full Professor in Statistical Science at University of Toronto, and has been selected into the National Talents Program of China. He has served as the Editor for Canadian Journal of Statistics (2019-2021), and is/was on editorial boards for a numebr of statistical journals, including the Annals of Statistics and Journal of the American Statistical Association.

Contact Person: ZHANG Rongmao(rmzhang@zju.edu.cn)