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April 2010 Covariate adjusted functional principal components analysis for longitudinal data
Ci-Ren Jiang, Jane-Ling Wang
Ann. Statist. 38(2): 1194-1226 (April 2010). DOI: 10.1214/09-AOS742

Abstract

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the first approach, both the mean and covariance functions depend on the covariate Z and time scale t while in the second approach only the mean function depends on the covariate Z. Both new approaches accommodate additional measurement errors and functional data sampled at regular time grids as well as sparse longitudinal data sampled at irregular time grids. The first approach to fully adjust both the mean and covariance functions adapts more to the data but is computationally more intensive than the approach to adjust the covariate effects on the mean function only. We develop general asymptotic theory for both approaches and compare their performance numerically through simulation studies and a data set.

Citation

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Ci-Ren Jiang. Jane-Ling Wang. "Covariate adjusted functional principal components analysis for longitudinal data." Ann. Statist. 38 (2) 1194 - 1226, April 2010. https://doi.org/10.1214/09-AOS742

Information

Published: April 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1183.62102
MathSciNet: MR2604710
Digital Object Identifier: 10.1214/09-AOS742

Subjects:
Primary: 62H25 , 62M15
Secondary: 62G20

Keywords: Functional data analysis , functional principal components analysis , local linear regression , longitudinal data analysis , smoothing , sparse data

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 2 • April 2010
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