  Observations which are realizations from some continuous process are frequent
in sciences, engineering, economics, and other fields. We consider linear
models, with possible random effects, where the responses are random functions
in a suitable Sobolev space. The processes cannot be observed directly. With
smoothing procedures from the original data, both the response curves and their
derivatives can be reconstructed, even separately. From both these samples of
functions, just one sample of representatives is obtained to estimate the
vector of functional parameters. A simulation study shows the benefits of this
approach over the common method of using information either on curves or
derivatives. The main theoretical result is a strong functional version of the
Gauss-Markov theorem. This ensures that the proposed functional estimator is
more efficient than the best linear unbiased estimator based only on curves or
derivatives.
