Deconvolution density estimation with penalised MLE

TL;DR

This paper introduces a new deconvolution density estimation method using penalised maximum likelihood, which outperforms existing Fourier-based methods especially with small samples or low signal-noise ratios.

Contribution

The paper proposes a novel penalised MLE approach for deconvolution density estimation, addressing instability issues of traditional Fourier-based methods.

Findings

Significantly better performance with small sample sizes.

More stable estimates at low signal-noise ratios.

Outperforms existing Fourier-based methods.

Abstract

Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all methods in the literature are based on Fourier transformation because it is mathematically a very neat solution. However, in practice these methods are unstable, and produce bad estimates when signal-noise ratio or sample size are low. In this paper, we develop a new deconvolution method based on maximum likelihood with a smoothness penalty. We show that our new method has much better performance than existing methods, particularly for small sample size or signal-noise ratio.