Statistica Sinica 19 (2009), 667-684
WAVELET ESTIMATIONS
FOR LONGITUDINAL DATA
Trung Tu Nguyen
University of Paris VII
Abstract: In the context of longitudinal data
analysis, we study a random function 
that represents patients or
subjects observed at randomly distributed points. Principal
components analysis (PCA) is useful in understanding the random
effects of . In this paper, we estimate the mean and covariance
functions of by wavelet methods. Proposed wavelet estimators
give interesting performances over a wide class of functions, even
if the regularity parameters of the original functions are not
assumed to be greater than 
. In another problem of longitudinal
analysis, we study the regression of observations at recorded times,
when the number of observations per unit is assumed to be a finite
integer. In this context, under Gaussian assumptions, our wavelet
estimator could be proved to be optimal.
Key words and phrases: Karhunen-Loève expansion,
nonparametric estimation, projection estimation, principal
components methods, wavelet decomposition.