Automatic estimation procedure in partial linear model with functional data

Partial linear modelling ideas have recently been adapted to situations when functional data are observed. This paper aims to complete the study of such model by proposing a fully automatic estimation procedure. This is achieved by constructing a data-driven method to choose the smoothing parameters entered in the nonparametric components of the model. The asymptotic optimality of the method is stated and its practical interest is illustrated on finite size Monte Carlo simulated samples.