Further theoretical and practical insight to the do-validated bandwidth selector

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. and that the recent do-validated method seems to provide the most practical alternative among these methods. In this paper we show step by step how classical cross-validation improves in theory, as well as in practice, from indirectness and that do-validated estimators improve in theory, but not in practice, from further indirectness. This paper therefore provides a strong support for the practical and theoretical properties of do-validated bandwidth selection. Do-validation is currently being introduced to survival analysis in a number of contexts and this paper provides evidence that this might be the immediate step forward. Permanent repository link

Double One-sided Cross-validation of Local Linear Hazards

“…This factor depends only on the kernels K andK Å L . Mammen et al (2011Mammen et al ( , 2014 provided the exact calculation of this factor for the Epanechnikov kernel and the quartic kernel (in the density case and under the IID formulation). These calculations can be used to compare the asymptotic performance of the bandwidth selectors.…”

“…Further insight for kernel density estimation was added into this discussion by Mammen et al . (). DO‐validation is perhaps the simplest possible exploitation of indirect cross‐validation originally developed by Hart and Lee (), Hart and Yi () and Savchuk et al .…”

“…Mammen et al . () developed a class of indirect cross‐validation procedures where the limit of the theoretical performance is as good as in infeasible plug‐in methods. In other words, a feasible indirect cross‐validation procedure does exist with the same theoretical performance as the infeasible plug‐in estimator.…”

“…The original paper on DO-validating density estimators of IID stochastic variables, Mammen et al (2011), concluded that infeasible plug-in outperforms DO-validation a little in theory and finite sample studies and that plug-in validation looses its good performance when transferred from infeasible to feasible implementations, at least for kernel density estimation. Further insight for kernel density estimation was added into this discussion by Mammen et al (2014). DO-validation is perhaps the simplest possible exploitation of indirect cross-validation originally developed by Hart and Lee (2005), Hart and Yi (1998) and Savchuk et al (2008Savchuk et al ( , 2010.…”

“…Indirect cross-validation transfers the smoothing optimization problem at hand to a more complicated problem, where the optimal level of smoothing is easier to obtain. Mammen et al (2014) developed a class of indirect cross-validation procedures where the limit of the theoretical performance is as good as in infeasible plug-in methods. In other words, a feasible indirect crossvalidation procedure does exist with the same theoretical performance as the infeasible plug-in estimator.…”