Functional Regression and Principal Components Analysis for
Sparse Longitudinal Data


Jane-Ling Wang

Univ. of California, Davis


We propose a nonparametric method to perform functional regression
and principal components analysis for sparse longitudinal data that
consist of noisy measurements with underlying smooth random
trajectories for each subject in a sample. The number of repeated
measurements available per subject is typically small, and their
spacing is irregular. Our method includes determination of the most
appropriate function base from the data and the associated
coefficients of the basis functions for each individual.

The proposed method easily handles situations where for most subjects
not more than two measurements are available. It is also suitable for
functional regression where both the predictor and response are
functions of a covariate such as time.  Asymptotic properties are
investigated under mild conditions, using tools from functional
analysis.  We illustrate the methods with a simulation study,
longitudinal CD4 data in AIDS patients and a functional regression
analysis of the dynamic relationship of immunoproteins albumin
and CRP.n

This is joint work with Fang Yao, UC Davis and Colorado State Univ.
and Hans-Georg Mueller -- University of California, Davis