Strong uniform consistency of nonparametric estimation of the censored conditional mode function

Let (T n ) n≥1 be a sequence of independent and identically distributed of interest random variables and (X n ) n≥1 be a sequence of covariates. In the censorship model, the random variable T is subject to random censoring by another random variable C. Let Θ(x) be the conditional mode function of T given X = x. In this article, we define a new kernel estimator Θ n (x) of Θ(x) and we establish the uniform strong consistency with a rate of convergence.