Estimator selection with respect to Hellinger-type risks

TL;DR

This paper introduces a flexible estimator selection method for various statistical problems involving the estimation of an intensity measure, using Hellinger-type risks, applicable to density, marginal, mean, and Poisson process intensity estimation.

Contribution

It proposes a novel estimator selection procedure based on the observed data, applicable across multiple estimation problems, and offers an alternative to existing T-estimators.

Findings

The method effectively performs model selection in diverse settings.

It provides a unified approach for estimator selection across different statistical problems.

The procedure demonstrates competitive performance compared to traditional methods.

Abstract

We observe a random measure $N$ and aim at estimating its intensity $s$. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random vector with nonnegative components and the intensity of a Poisson process. Our estimation strategy is based on estimator selection. Given a family of estimators of $s$ based on the observation of $N$, we propose a selection rule, based on $N$ as well, in view of selecting among these. Little assumption is made on the collection of estimators. The procedure offers the possibility to perform model selection and also to select among estimators associated to different model selection strategies. Besides, it provides an alternative to the $T$-estimators as studied recently in Birg\'e (2006). For illustration, we consider the problems of estimation and (complete) variable selection in various regression settings.