A note on estimating the conditional expectation under censoring and association: strong uniform consistency

Abstract

Let $$\left\{ (X_{i},Y_{i}), i \ge 1 \right\} $$ be a strictly stationary sequence of associated random vectors distributed as (X, Y). This note deals with kernel estimation of the regression function $$r(x)=\mathbb {E}[Y|X=x]$$ in the presence of randomly right censored data caused by another variable C. For this model we establish a strong uniform consistency rate of the proposed estimator, say $$r_{n}(x)$$ . Simulations are drawn to illustrate the results and to show how the estimator behaves for moderate sample sizes.