Wavelet Regression Estimation in Nonparametric Mixed Effect Models

We show that a nonparametric estimator of a regression function, obtained as solution of a specific regularization problem is the bestlinear 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 non equispaced design. Numerical experiments are presented both on simulated and ERP real data.