Uniform rate of strong consistency for a smooth kernel estimator of the conditional mode for censored time series

Let (Tn)n⩾1 be a sequence random variables (rvs) of interest distributed as T. In censorship models the rv T is subject to random censoring by another rv C. We consider the problem of estimating its conditional mode function, given a vector of covariates X. Let θ(x) be the mode of the density of T given X=x. In this paper we consider a kernel estimator θ^n(x) of θ(x) and establish its almost sure convergence with rate under an α-mixing condition.