A new V-fold type procedure based on robust tests

TL;DR

This paper introduces a novel V-fold cross-validation method based on robust tests, providing theoretical guarantees, a fast algorithm, and demonstrating its effectiveness in density estimation and bandwidth selection through simulations.

Contribution

It presents a new V-fold procedure based on robust tests, extending existing methods with theoretical analysis and practical algorithms.

Findings

The method satisfies an oracle inequality under weak assumptions.

It performs well in density estimation and bandwidth selection tasks.

The empirical study shows the influence of V on risk and compares favorably with classical methods.

Abstract

We define a general V-fold cross-validation type method based on robust tests, which is an extension of the hold-out defined by Birg{\'e} [7, Section 9]. We give some theoretical results showing that, under some weak assumptions on the considered statistical procedures, our selected estimator satisfies an oracle type inequality. We also introduce a fast algorithm that implements our method. Moreover we show in our simulations that this V-fold performs generally well for estimating a density for different sample sizes, and can handle well-known problems, such as binwidth selection for histograms or bandwidth selection for kernels. We finally provide a comparison with other classical V-fold methods and study empirically the influence of the value of V on the risk.