Non-parametric estimation of the average growth curve from quantized observations and correlated errors

In this Note, we consider the problem of estimating the regression function for a fixed design model, when we only have access to quantized and correlated data. In order for the constructed estimate to be consistent, we assume that repeated observations are available. We give the asymptotic performance in terms of the mean squared error for the regression function estimator constructed from quantized observations, and we generate the optimal bandwidth. (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.