Generalized cross-validation for wavelet shrinkage in nonparametric mixed effects models

Abstract

A nonlinear wavelet shrinkage estimator was proposed in an earlier article by Huang and Lu. Such an estimator combined the asymptotic equivalence to the best linear unbiased prediction and the Bayesian estimation in nonparametric mixed-effects models. In this article, a data-driven GCV method is proposed to select hyperparameters. The proposed GCV method has low computational cost and can be applied to one or higher dimensional data. It can be used for selecting hyperparameters for either level independent or level dependent shrinkage. It can also be used for selecting the primary resolution level and the number of vanishing moments in the wavelet basis. The strong consistency of the GCV method is proved.