On Estimation of the Effect Lag of Predictors and Prediction in a Functional Linear Model

We propose a functional linear model to predict a functional response using multiple functional and longitudinal predictors and to estimate the effect lags of predictors. The coefficient functions are written as the expansion of a basis system (e.g. functional principal components, splines), and the coefficients of the basis functions are estimated via optimizing a penalization criterion. Then effect lags are determined by simultaneously searching on a prior designed grid mesh based on minimization of a proposed prediction error criterion. Mathematical properties of the estimated regression functions and predicted responses are studied. The performance of the method is evaluated by extensive simulations and a real data analysis application on chronic obstructive pulmonary disease (COPD).