Alexander Goldenshluger
University of Haifa, Israel
Density deconvolution under general assumptions
Abstract:
We study the problem of density deconvolution under general assumptions on the
measurement error distribution. Typically deconvolution estimators are constructed
using Fourier transform techniques, and it is assumed that the characteristic
function of the measurement errors does not have zeros on the real line. This
assumption is rather strong and is not fulfilled in many cases of interest.
In this paper we develop a methodology for constructing optimal density deconvolution
estimators in the general setting that covers vanishing and non-vanishing
characteristic functions of the measurement errors. We derive upper bounds on the
risk of the proposed estimators and provide sufficient conditions under which
zeros of the corresponding characteristic function have no effect on estimation
accuracy. Moreover, we show that the derived conditions are also necessary in some
specific problem instances.
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