Spring Seminar Series  February 22, 2007
University of Minnesota
School of Statistics
College of Liberal Arts

Iterative Functional Principal Component Analysis for Correlation Reduction

Fang Yao
Department of Statistics
University of Toronto

Thursday, February 22, 2007
3:30 PM, 115 Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall


Abstract

In this talk we propose an iterative estimation procedure for performing functional principal component analysis. The procedure aims at functional  or longitudinal data where the repeated measurements from the same subject are correlated.  For the handling of the within-subject correlation, we develop an iterative procedure which would gradually reduce the dependence amongst the repeated measurements made for the same subject. An increasingly popular smoothing approach, penalized spline regression, is used to represent the mean trend. This allows straightforward incorporation of covariates and simple implementation of inference procedures for coefficients. The resulting data after iteration are theoretically shown to be asymptotically independent, which suggests that the general theory of penalized spline regression developed for independent data can also be applied to functional data.  The effectiveness of the proposed procedure is demonstrated via a simulation study and an application to yeast cell cycle data.