Copyright © 2011 Frits Ruymgaart et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Exploiting an expansion for analytic functions of operators, the asymptotic distribution of an estimator of the functional regression parameter is obtained in a rather simple way; the result is applied to testing linear hypotheses. The expansion is also used to obtain a quick proof for the asymptotic optimality of a functional classification rule, given Gaussian populations.