Functional
Regression and Principal Components Analysis
For Sparse longitudinal Data |
Fang
Yao
University of California-Davis
Friday,
14 February 2003
3:10 PM
E103 Engineering
ABSTRACT
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
proposal includes determination of the most appropriate function basis
from the data. The proposed conditional method is simple and straightforward
to implement and includes estimation of the covariance structure and
of the variance of the measurements. It is also suitable for functional
regression where both the predictor and response are functions of a
covariate such as time. The resulting technique is flexible and allows
for different timing of measurements for predictor and response functions.
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.
Key Words: Functional Data, Nonparametric Functional Regression,
Refreshments will be served at 2:45 p.m. in Room 008 of the Statistics
Building
