Abstract
Let (X-i, Y-l)(i=1,...,n) be a sequence of stationary ergodic processes valued in F x R, where is a semi-metric space. We consider the problem of estimating the regression function of Y-i given X-i by the robust M-estimation method. The principal aim of this work is to prove the almost complete convergence (with rate) for the proposed estimator. This result is obtained under a stationary ergodic process assumption, without using traditional mixing conditions. (C) 2012 Elsevier B.V. All rights reserved.