Open Access
2016 Nonparametric Laguerre estimation in the multiplicative censoring model
Denis Belomestny, Fabienne Comte, Valentine Genon-Catalot
Electron. J. Statist. 10(2): 3114-3152 (2016). DOI: 10.1214/16-EJS1203


We study the model $Y_{i}=X_{i}U_{i},\;i=1,\ldots,n$ where the $U_{i}$’s are i.i.d. with $\beta(1,k)$ density, $k\ge1$, $k$ integer, the $X_{i}$’s are i.i.d., nonnegative with unknown density $f$. The sequences $(X_{i}),(U_{i}),$ are independent. We aim at estimating $f$ on ${\mathbb{R}}^{+}$ from the observations $(Y_{1},\dots,Y_{n})$. We propose projection estimators using a Laguerre basis. A data-driven procedure is described in order to select the dimension of the projection space, which performs automatically the bias variance compromise. Then, we give upper bounds on the ${\mathbb{L}}^{2}$-risk on specific Sobolev-Laguerre spaces. Lower bounds matching with the upper bounds within a logarithmic factor are proved. The method is illustrated on simulated data.


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Denis Belomestny. Fabienne Comte. Valentine Genon-Catalot. "Nonparametric Laguerre estimation in the multiplicative censoring model." Electron. J. Statist. 10 (2) 3114 - 3152, 2016.


Received: 1 May 2016; Published: 2016
First available in Project Euclid: 10 November 2016

zbMATH: 1357.62160
MathSciNet: MR3571964
Digital Object Identifier: 10.1214/16-EJS1203

Primary: 62G07

Keywords: adaptive estimation , lower bounds , Model selection , Multiplicative censoring , projection estimator

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.10 • No. 2 • 2016
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