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Regular version of the site

Article

Density deconvolution under general assumptions

In  this paper 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.