ST ] 2 2 M ay 2 00 3 Asymptotic Normality of Nonparametric Kernel Type Deconvolution Density Estimators : crossing the Cauchy boundary

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 λ-stable distribution with 0 < λ ≤ 2. It turns out that the limit behavior changes if the exponent parameter λ passes the value one, the case of Cauchy deconvolution. AMS classification: primary 62G05; secondary 62E20