Asymptotic Normality of Nonparametric Kernel Type Deconvolution Density Estimators: crossing the Cauchy boundary

A. J. van Es, H. -W. Uh

Published 2002-12-01, updated 2003-05-22Version 2

We derive asymptotic normality of kernel type deconvolution density estimators. In particular we consider deconvolution problems where the known component of the convolution has a symmetric lambda-stable distribution, 0<lambda<= 2. It turns out that the limit behavior changes if the exponent parameter lambda passes the value one, the case of Cauchy deconvolution.