Electronic Journal of Statistics

Nonparametric Laguerre estimation in the multiplicative censoring model

Denis Belomestny, Fabienne Comte, and Valentine Genon-Catalot

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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.

Article information

Electron. J. Statist., Volume 10, Number 2 (2016), 3114-3152.

Received: May 2016
First available in Project Euclid: 10 November 2016

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Zentralblatt MATH identifier

Primary: 62G07: Density estimation

Adaptive estimation lower bounds model selection multiplicative censoring projection estimator


Belomestny, Denis; Comte, Fabienne; Genon-Catalot, Valentine. Nonparametric Laguerre estimation in the multiplicative censoring model. Electron. J. Statist. 10 (2016), no. 2, 3114--3152. doi:10.1214/16-EJS1203. https://projecteuclid.org/euclid.ejs/1478747031

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