Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem

• 成果类型: Article
• 署名作者: Delaigle, Aurore; Hall, Peter
• 署名单位: University of Melbourne; University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.857611
• 发表日期: 2014
• 页码: 717-729
• 关键词: Asymptotic Normality; measurement error; Optimal Rates; regression; CONVERGENCE; likelihood

摘要

Nonparametric estimation of a density from contaminated data is a difficult problem, for which convergence rates are notoriously slow. We introduce parametrically assisted nonparametric estimators which can dramatically improve on the performance of standard nonparametric estimators when the assumed model is close to the true density, without degrading much the quality of purely nonparametric estimators in other cases. We establish optimal convergence rates for our problem and discuss estimators that attain these rates. The very good numerical properties of the methods are illustrated via a simulation study. Supplementary materials for this article are available online.