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Penalized spline models for functional principal component analysis
Author(s) -
Yao Fang,
Lee Thomas C. M.
Publication year - 2006
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00530.x
Subject(s) - functional principal component analysis , principal component analysis , spline (mechanical) , smoothing spline , functional data analysis , smoothing , covariate , inference , mathematics , computer science , b spline , algorithm , mathematical optimization , data set , statistics , artificial intelligence , mathematical analysis , structural engineering , engineering , bilinear interpolation , spline interpolation
Summary. 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. An increasingly popular smoothing approach, penalized spline regression, is used to represent the mean function. This allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for coefficients. For the handling of the within‐subject correlation, we develop an iterative procedure which reduces the dependence between the repeated measurements that are made for the same subject. The resulting data after iteration are theoretically shown to be asymptotically equivalent (in probability) to a set of independent data. This suggests that the general theory of penalized spline regression that has been 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 gene expression data.