  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.
