Sharp Optimality in Density Deconvolution with Dominating Bias. I

摘要

We consider estimation of the common probability density f of independent identically distributed random variables X_i that are observed with an additive independent identically distributed noise. We assume that the unknown density f belongs to a class {cal A} of densities whose characteristic function is described by the exponent exp(-lpha |u|^r) as |u|oinfty, where lpha>0, r>0. The noise density assumed known and such that its characteristic function decays as exp (-eta|u|^s), as |u|oinfty, where eta>0, s>0. Assuming that r