Some asymptotic theory for functional regression and classification

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. © 2011 Frits Ruymgaart et al.