Adaptive Deconvolution on the Nonnegative Real Line

Gwennaëlle Mabon ()
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Gwennaëlle Mabon: CREST

No 2014-40, Working Papers from Center for Research in Economics and Statistics

Abstract: In this paper we consider the problem of adaptive density or survival function estimation in an additive model de ned by Z = X + Y with X independent of Y , when both random variables are nonnegative. We want to recover the distribution of X (density or survival function) through n observations of Z, assuming that the distribution of Y is known. This issue can be seen as the classical statistical problem of deconvolution which has been tackled in many cases using Fourier-type approaches. Nonetheless, in the present case the random variables have the particularity to be R+ supported. Knowing that, we propose a new angle of attack by building a projection estimator with an appropriate Laguerre basis. We present upper bounds on the mean squared integrated risk of our density and survival function estimators. We then describe a nonparametric adaptive strategy for selecting a relevant projection space. The procedures are illustrated with simulated data and compared to the performances of more classical deconvolution setting using a Fourier approach.

Keywords: Inverse; problem.; Adaptive; estimation.; Nonparametric; density; estimation.; Survival; function; estimation.; Laguerre; basis.; Deconvolution.; Mean; squared; risk. (search for similar items in EconPapers)
Pages: 25
Date: 2014-10
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