Influence in the functional linear model with scalar response

Abstract

This paper studies how to identify influential curves in the functional linear model in which the response is scalar and the predictor is functional and how to measure their effects on the estimation of the model and on the forecasts, when the model is estimated by the principal components method. For that, we introduce and analyze two statistics that measure the influence of each curve on the functional slope estimate of the model, which are generalizations of the measures proposed for the standard regression model by Cook (1977) and Peña (2005), respectively.