Statistica Sinica

Trung Tu Nguyen

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.