Adaptive estimation in regression for discretized functional data.
Abstract
My presentation will focus on functional data, that is, data taking the form of functions. In practice, such data are never observed continuously, but rather in a discretized and often noisy form. I will specifically examine the impact of this discretization on estimation in the scalar-on-function linear model. My approach first consists in reconstructing the curves from the discrete observations, and then estimating the model using a penalized regression method with model selection. I will present theoretical results, in particular oracle inequalities and convergence rates, which highlight the role of the number of observation points. Finally, an application to energy consumption data will illustrate these results.