Simultaneous non-parametric regressions of unbalanced longitudinal data. (English) Zbl 0900.62199

Besse, Philippe C.; Cardot, Hervé; Ferraty, Frédéric

Comput. Stat. Data Anal. 24, No. 3, 255-270 (1997).

Summary: The aim of this paper is to simultaneously estimate n curves corrupted by noise, this means several observations of a random process. The non-parametric estimation of the sampled paths leads to a new kind of functional principal components analysis which simultaneously takes into account a dimensionality and a smoothness constraint. Furthermore, the use of B-spline approximation to estimate the curves allows the study of unbalanced longitudinal data. The relationship between the choice of the smoothing parameter and that of dimensionality is discussed. A simulation study shows good behaviors of this proposed estimate compared to n independent smoothing splines under generalized cross-validation. Finally, the methodology of this paper is illustrated by its application to a real world data set.

MSC:

62G07	Density estimation
65C99	Probabilistic methods, stochastic differential equations

Keywords:

Non-parametric regression; Functional principal component analysis; Hybrid splines; B-splines; Rainfall data

Software:

R

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