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Pré-Publication, Document De Travail Année : 2019

Nonparametric relative error estimation of the regression function for censored data

Résumé

Let $ (T_i)_{i }$ be a sequence of independent identically distributed (i.i.d.) random variables (r.v.) of interest distributed as $ T$ and $(X_i)_{ i }$ be a corresponding vector of covariates taking values on $ \mathbb{R}^d$. In censorship models the r.v. $ T$ is subject to random censoring by another r.v. $ C$. In this paper we built a new kernel estimator based on the so-called synthetic data of the mean squared relative error for the regression function. We establish the uniform almost sure convergence with rate over a compact set and its asymptotic normality. The asymptotic variance is explicitly given and as product we give a confidence bands. A simulation study has been conducted to comfort our theoretical results
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Dates et versions

hal-01994512 , version 1 (25-01-2019)

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Feriel Bouhadjera, Elias Ould Saïd, Mohamed Riad Remita. Nonparametric relative error estimation of the regression function for censored data. 2019. ⟨hal-01994512⟩
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