Non-parametric regression with dependent censored data

Abstract

Let (X-i,Y-i) (i=1,...,n) be n replications of a random vector (X,Y ), where Y is supposed to be subject to random right censoring. The data (X-i,Y-i) are assumed to come from a stationary alpha-mixing process. We consider the problem of estimating the function m(x) = E(phi(Y) vertical bar X=x), for some known transformation phi. This problem is approached in the following way: first, we introduce a transformed variable Y-i*, that is not subject to censoring and satisfies the relation E(phi(Y-i) vertical bar X-i = x) = E(phi(Y-i* vertical bar X-i = x)and then we estimate m(x) by applying local linear regression techniques. As a by-product, we obtain a general result on the uniform rate of convergence of kernel type estimators of functionals of an unknown distribution function, under strong mixing assumptions.