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April 2009 Estimating a concave distribution function from data corrupted with additive noise
Geurt Jongbloed, Frank H. van der Meulen
Ann. Statist. 37(2): 782-815 (April 2009). DOI: 10.1214/07-AOS579


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, ∞). 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.


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Geurt Jongbloed. Frank H. van der Meulen. "Estimating a concave distribution function from data corrupted with additive noise." Ann. Statist. 37 (2) 782 - 815, April 2009.


Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62029
MathSciNet: MR2502651
Digital Object Identifier: 10.1214/07-AOS579

Primary: 62E20 , 62G05

Keywords: asymptotic distribution , Deconvolution , decreasing density , least squares , maximum likelihood , minimax risk

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 2 • April 2009
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