Nonparametric relative error estimation of the regression function for censored data
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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 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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