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a b s t r a c tLet (T i ) 1≤i≤n be a sample of independent and identically distributed (iid) random variables (rv) of interest and (X i ) 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 estimatorθ n (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.

This paper investigates the conditional quantile estimation of a randomly censored scalar response variable given a functional random covariate (i.e. valued in some infinite-dimensional space) whenever a stationary ergodic data are considered. A kernel-type estimator of the conditional quantile function is introduced. Then, a strong consistency rate as well as the asymptotic distribution of the estimator are established under mild assumptions. A simulation study is considered to show the performance of the proposed estimator. An application to the electricity peak demand prediction using censored smart meter data is also provided.

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In this paper, we investigate the problem of the local linear estimation of the conditional ageing intensity function, when the variable of interest is subject to random right-censored. We establish under appropriate conditions the asymptotic normality of this estimator.