Non‐parametric Regression with Dependent Censored Data

Abstract

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 α ‐mixing process. We consider the problem of estimating the function m ( x ) =ℰ( φ ( Y ) | X = x ), for some known transformation φ . This problem is approached in the following way: first, we introduce a transformed variable , that is not subject to censoring and satisfies the relation , 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.