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

Let ( T n ) 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.