# Bandwidth Selection for the Wolverton-Wagner Estimator

## TL;DR

This paper investigates bandwidth selection methods for the Wolverton-Wagner estimator, providing theoretical controls on its mean squared and integrated mean squared errors, and introduces adaptive estimators for the smoothness parameter.

## Contribution

It introduces new adaptive bandwidth selection techniques for the Wolverton-Wagner estimator using Goldenshluger-Lepski and Lacour-Massart-Rivoirard methods, with numerical validation.

## Key findings

- Theoretical bounds on MSE and MISE for the estimator.
- Development of adaptive estimators for the smoothness parameter.
- Numerical experiments demonstrating the effectiveness of the proposed methods.

## Abstract

For $n$ independent random variables having the same H\"older continuous density, this paper deals with controls of the Wolverton-Wagner's estimator MSE and MISE. Then, for a bandwidth $h_n(\beta)$, estimators of $\beta$ are obtained by a Goldenshluger-Lepski type method and a Lacour-Massart-Rivoirard type method. Some numerical experiments are provided for this last method.