Prediction in functional regression with discretely observed and noisy covariates

Abstract

Consider discretely sampled and noisy functional data as explanatory variables in a linear regression. If the primary goal is prediction, then it is argued that the practical gain of embedding the problem into a scalar-on-function regression is limited. Instead, the approximate factor model structure of the predictors is employed and the response is regressed on an appropriate number of factor scores. This approach is shown to be consistent under mild technical assumptions, it is numerically efficient, and it yields good practical performance in both, simulations and real data settings.