# Density Deconvolution for Generalized Skew-Symmetric Distributions

## TL;DR

This paper introduces a new density deconvolution estimator for generalized skew-symmetric distributions, combining kernel methods and GMM, with proven theoretical properties and superior simulation performance.

## Contribution

It develops a novel GSS deconvolution estimator with bandwidth selection, GMM-based parameter estimation, and solution criteria, advancing existing nonparametric methods.

## Key findings

- GSS estimator outperforms nonparametric deconvolution in simulations
- Derived MISE for the GSS estimator provides theoretical insight
- Proposed bandwidth and solution criteria improve estimation stability

## Abstract

This paper develops a density deconvolution estimator that assumes the density of interest is a member of the generalized skew-symmetric (GSS) family of distributions. Estimation occurs in two parts: a skewing function, as well as location and scale parameters must be estimated. A kernel method is proposed for estimating the skewing function. The mean integrated square error (MISE) of the resulting GSS deconvolution estimator is derived. Based on derivation of the MISE, two bandwidth estimation methods for estimating the skewing function are also proposed. A generalized method of moments (GMM) approach is developed for estimation of the location and scale parameters. The question of multiple solutions in applying the GMM is also considered, and two solution selection criteria are proposed. The GSS deconvolution estimator is further investigated in simulation studies and is compared to the nonparametric deconvolution estimator. For most simulation settings considered, the GSS estimator has performance superior to the nonparametric estimator.