The Annals of Statistics

Covariate adjusted functional principal components analysis for longitudinal data

Ci-Ren Jiang and Jane-Ling Wang

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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.

Article information

Ann. Statist., Volume 38, Number 2 (2010), 1194-1226.

First available in Project Euclid: 19 February 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H25: Factor analysis and principal components; correspondence analysis 62M15: Spectral analysis
Secondary: 62G20: Asymptotic properties

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


Jiang, Ci-Ren; Wang, Jane-Ling. Covariate adjusted functional principal components analysis for longitudinal data. Ann. Statist. 38 (2010), no. 2, 1194--1226. doi:10.1214/09-AOS742.

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