Covariate adjusted functional principal components analysis for longitudinal data. (English) Zbl 1183.62102

Jiang, Ci-Ren; Wang, Jane-Ling

Ann. Stat. 38, No. 2, 1194-1226 (2010).

Summary: 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.

MSC:

62H25	Factor analysis and principal components; correspondence analysis
62M15	Inference from stochastic processes and spectral analysis
62G20	Asymptotic properties of nonparametric inference
65C60	Computational problems in statistics (MSC2010)

Keywords:

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

Software:

fda (R)

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