Density Deconvolution with Additive Measurement Errors using Quadratic Programming

TL;DR

This paper introduces a quadratic programming-based density deconvolution method that outperforms kernel methods, effectively handling noise and incorporating various distribution constraints for improved estimation accuracy.

Contribution

The authors develop a novel quadratic programming approach for density deconvolution that improves estimation accuracy and flexibility over existing kernel-based methods.

Findings

Quadratic programming method achieves better estimation than kernel methods.

Incorporating distribution constraints enhances estimation accuracy.

Method performs well with common constraints like nonnegativity and unimodality.

Abstract

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can achieve better estimation than kernel density deconvolution methods. The QP approach appears to have a more favorable regularization tradeoff between oversmoothing vs. oscillation, especially at the tails of the distribution. An additional advantage is that it is straightforward to incorporate a number of common density constraints such as nonnegativity, integration-to-one, unimodality, tail convexity, tail monotonicity, and support constraints. We demonstrate that the QP approach has outstanding estimation performance relative to existing methods. Its performance is superior when only the universally applicable nonnegativity and integration-to-one constraints are incorporated, and incorporating additional common constraints when applicable (e.g., nonnegative support, unimodality, tail monotonicity or convexity, etc.) can further substantially improve the estimation.