Weak convergence of the supremum distance for supersmooth kernel deconvolution

TL;DR

This paper investigates the asymptotic behavior of the maximum deviation of supersmooth deconvolution kernel density estimators from their expected value, revealing distinct asymptotics compared to ordinary smooth cases.

Contribution

It provides the first derivation of the asymptotic distribution of the supremum distance for supersmooth deconvolution kernel estimators, highlighting fundamental differences from ordinary smooth scenarios.

Findings

Asymptotic distribution derived for supersmooth deconvolution estimators

Distinct asymptotic behavior compared to ordinary smooth deconvolution

Enhances understanding of supremum distance in deconvolution problems

Abstract

We derive the asymptotic distribution of the supremum distance of the deconvolution kernel density estimator to its expectation for certain supersmooth deconvolution problems. It turns out that the asymptotics are essentially different from the corresponding results for ordinary smooth deconvolution.