Wavelet regression estimation in nonparametric mixed effect models

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Abstract

We show that a nonparametric estimator of a regression function, obtained as solution of a specific regularization problem is the best linear unbiased predictor in some nonparametric mixed effect model. Since this estimator is intractable from a numerical point of view, we propose a tight approximation of it easy and fast to implement. This second estimator achieves the usual optimal rate of convergence of the mean integrated squared error over a Sobolev class both for equispaced and nonequispaced design. Numerical experiments are presented both on simulated and ERP real data. © 2003 Elsevier Science (USA). All rights reserved.

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Angelini, C., De Canditiis, D., & Leblanc, F. (2003). Wavelet regression estimation in nonparametric mixed effect models. Journal of Multivariate Analysis, 85(2), 267–291. https://doi.org/10.1016/S0047-259X(02)00055-6

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