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arXiv · 0904.0091

Estimating a concave distribution function from data corrupted with additive noise

Geurt Jongbloed·Frank H. van der Meulen
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Abstract

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 $(0,\infty)$. 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. 2009-04-01. Estimating a concave distribution function from data corrupted with additive noise. https://doi.org/10.1214/07-aos579

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