ESTIMATING A CONCAVE DISTRIBUTION FUNCTION FROM DATA CORRUPTED WITH ADDITIVE NOISE

• 成果类型: Article
• 署名作者: Jongbloed, Geurt; van der Meulen, Frank H.
• 署名单位: Delft University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS579
• 发表日期: 2009
• 页码: 782-815
• 关键词: nonparametric deconvolution; Optimal Rates; density; CONVERGENCE

摘要

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on (0, infinity). For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational algorithm. For the LS estimator and its derivative, we also derive the pointwise asymptotic distribution. Moreover, the rate n(-2/5) achieved by the LS estimator is shown to be minimax for estimating the distribution function at a fixed point.