Generalized linear model with functional covariate and its derivatives

A generalized functional linear regression model is proposed by considering a functional covariate and its derivatives as functional predictors. The unobserved derivatives of a random function may carry useful information and need to be estimated. We apply the notion of functional principal component analysis to modeling functional predictors. The proposed regression model is parameterized in various ways to investigate the effect of each functional predictor. The performance of the proposed method is demonstrated through a traffic data example.補正完