Abstract
This paper deals with the problem of estimating the regression of a surrogated scalar response variable given a functional random one. We construct an estimator of the regression operator by using, in addition to the available (true) response data, a surrogate data. We then establish some asymptotic properties of the constructed estimator in terms of the almost-complete and the quadratic mean convergences. Notice that the obtained results generalize a part of the results obtained in the finite dimensional framework. Finally, an illustration on the applicability of our results on both simulated data and a real dataset was realized. We have thus shown the superiority of our estimator on classical estimators when we are lacking complete data.