Estimating a concave distribution function from data corrupted with additive noise
Geurt Jongbloed, Frank H. van der Meulen
The Annals of Statistics · 2009 · Volume 37 · Issue 2
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, ∞). 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.
Keywords
62E20, 62G05, asymptotic distribution, Deconvolution, decreasing density, least squares, maximum likelihood, minimax risk
Enable JavaScript for citation tools and additional paper interactions.