Deconvolution density estimation with heteroscedastic errors using SIMEX

TL;DR

This paper introduces a fast SIMEX-based method for density estimation with heteroscedastic measurement errors, demonstrating improved accuracy over traditional Fourier deconvolution in simulations and real data.

Contribution

The paper develops a novel SIMEX algorithm tailored for heteroscedastic errors, providing theoretical consistency, asymptotic variance, and practical smoothing parameter selection.

Findings

Proposed method outperforms Fourier deconvolution in simulations.

The estimator is shown to be consistent with known asymptotic properties.

Application to real data illustrates practical effectiveness.

Abstract

In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. In this paper, we propose a fast algorithm using a simulation-extrapolation (SIMEX) method to recover the unknown density in the case of heteroscedastic contamination. We show the consistency of the estimator and obtain its asymptotic variance and then address the practical selection of the smoothing parameter. We demonstrate that, through a finite sample simulation study, the proposed method performs better than the Fourier-type deconvolution method in terms of integrated squared error criterion. Finally, a real data application is conducted to illustrate the use of the method.