Work

Estimation for the convolution of several multidimensional densities

Year: 2025

Type: article

Abstract: This work is concerned with the problem of estimating the p-fold convolution of the densities of p independent random vectors in ℝd. Two nonparametric estimators are proposed, a kernel and a projection estimator, and their integrated quadratic risk is studied. We use Fourier analysis to bound the variance and consider Sobolev classes to discuss the convergence rates for both cases. In addition, we propose a fully data-driven kernel estimator based on a thresholding procedure and study model selection for the projection estimator. Finally, we illustrate the results in simulation experiments.

Source: Electronic Journal of Statistics

DOI: 10.1214/25-ejs2477

Authors: Fabienne Comte, Bianca Neubert

Institutions: Université Paris Cité, Mathématiques Appliquées à Paris 5, Heidelberg University

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

OpenAlex ID: W4414534559