DENSITY DECONVOLUTION UNDER GENERAL ASSUMPTIONS ON THE DISTRIBUTION OF MEASUREMENT ERRORS

• 成果类型: Article
• 署名作者: Belomestny, Denis; Goldenshluger, Alexander
• 署名单位: University of Duisburg Essen; University of Haifa; HSE University (National Research University Higher School of Economics)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS1969
• 发表日期: 2021
• 页码: 615-649
• 关键词: oracle inequalities; Optimal Rates; CONVERGENCE

摘要

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 nonvanishing 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.