文章基本信息

标题：Laplace deconvolution with noisy observations
本地全文：下载
作者：Felix Abramovich ; Marianna Pensky ; Yves Rozenholc 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：1094-1128
DOI：10.1214/13-EJS796
语种：English
出版社：Institute of Mathematical Statistics
摘要：In the present paper we consider Laplace deconvolution problem for discrete noisy data observed on an interval whose length $T_{n may increase with the sample size. Although this problem arises in a variety of applications, to the best of our knowledge, it has been given very little attention by the statistical community. Our objective is to fill the gap and provide statistical analysis of Laplace deconvolution problem with noisy discrete data. The main contribution of the paper is an explicit construction of an asymptotically rate-optimal (in the minimax sense) Laplace deconvolution estimator which is adaptive to the regularity of the unknown function. We show that the original Laplace deconvolution problem can be reduced to nonparametric estimation of a regression function and its derivatives on the interval of growing length $T_{n. Whereas the forms of the estimators remain standard, the choices of the parameters and the minimax convergence rates, which are expressed in terms of $T_{n}^{2}/n$ in this case, are affected by the asymptotic growth of the length of the interval.
关键词：Adaptivity;kernel estimation;minimax rates, Volterra equation;Laplace convolution.