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• W2551625435 abstract "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, $kge1$, $k$ 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." @default.
• W2551625435 created "2016-11-30" @default.
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• W2551625435 date "2016-01-01" @default.
• W2551625435 modified "2023-10-16" @default.
• W2551625435 title "Nonparametric Laguerre estimation in the multiplicative censoring model" @default.
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• W2551625435 doi "https://doi.org/10.1214/16-ejs1203" @default.
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