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Salah Khardani,Elias Ould Saïd,Mohamed Lemdani 한국통계학회 2010 Journal of the Korean Statistical Society Vol.39 No.4
Let (Ti)1≤i≤n be a sample of independent and identically distributed (iid) random variables (rv) of interest and (Xi)1≤i≤n be a corresponding sample of covariates. In censorship models the rv T is subject to random censoring by another rv C. Let θ(x) be the conditional mode function of the density of T given X = x. In this work we define a new smooth kernel estimator ˆθn(x) of θ(x) and establish its almost sure convergence and asymptotic normality. An application to prediction and confidence bands is also given. Simulations are drawn to lend further support to our theoretical results for finite sample sizes.
Mohammed Attouch,Ali Laksaci,Elias Ould Saïd 한국통계학회 2010 Journal of the Korean Statistical Society Vol.39 No.4
We propose a family of robust nonparametric estimators for a regression function based on the kernel method. We establish the asymptotic normality of the estimator under the concentration property on small balls probability measure of the functional explanatory variable when the observations exhibit some kind of dependence. This approach can be applied in time series analysis to make prediction and build confidence bands.Weillustrate our methodology on the US electricity consumption data.