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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 $X$ that represents patients or subjects observed at randomly distributed points. Principal components analysis (PCA) is useful in understanding the random effects of $X$. In this paper, we estimate the mean and covariance functions of $X$ 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 $2$. 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.

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