Exact bootstrap methods for non parametric curve estimationreducing the complexity of machine learning methods

Abstract

This thesis deals with bandwidth selection for nonparametric curve estimation. In particular, closed expressions for some error criteria of kernel estimators have been proposed. Additionally, bootstrap algorithms have been reviewed (or proposed) in order to derive exact formulas for the bootstrap version of the aforementioned error criteria. This is very useful because Monte Carlo approximation is no longer needed. Moreover, bandwidth selectors for the nonparametric curve estimators studied in this thesis have been de ned by means of minimizing these bootstrap exact formulas. Speci cally, we have dealt with bandwidth selection for nonparametric density estimation under dependence and hazard rate estimation. Moreover, we have dealt with bandwidth selection for statistical matching and prediction. In the last two contexts, the concept of proxy estimator is introduced in order to derive closed-form expressions for the bootstrap version of some error criteria. The good empirical behaviour of every method proposed in this thesis is empirically checked via simulations. Furthermore, all methods are illustrated with an application to real data sets. Asymptotic results in the context of bandwidth selection for prediction considering a Nadaraya-Watson proxy estimator is also included.