In the present paper we consider Laplace deconvolution on the basis of discrete noisy data observed on the interval which length may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge, it has not been systematically studied in statistical literature and the present paper contributes to fill this gap. We derive an adaptive kernel estimator of the function of interest, and establish its asymptotic minimaxity over a range of Sobolev classes. A limited simulation study shows that, in addition to providing theoretical asymptotic results, the proposed Laplace deconvolution estimator demonstrates good performance in finite sample examples.
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