Simultaneous non-parametric regressions of unbalanced longitudinal data

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 dimension...

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Bibliographic Details
Published in:Computational statistics & data analysis 1997-05, Vol.24 (3), p.255-270
Main Authors: Besse, Philippe C., Cardot, Hervé, Ferraty, Frédéric
Format: Article
Language:English
Subjects:
Approximation theory
B-splines
Computer simulation
Constraint theory
Data reduction
Estimation
Functional principal component analysis
Hybrid splines
Non-parametric regression
Q1
Rain
Rainfall data
Regression analysis
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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.
ISSN:0167-9473
1872-7352
DOI:10.1016/S0167-9473(96)00067-9