Abstract
Let (X-i, Y-i)(i=1,...,n) be a sequence of strongly mixing random vectors valued in F x R, where F is a Hilbert space. This note deals with the problem of the local linear estimation of the conditional cumulative distribution function of Y-i given X-i. Then, the main goals of this note are (i) to construct a fast kNN local linear estimate of the conditional distribution function, and (ii) to prove its strong consistency in the functional time series analysis situation. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.