The historical functional linear model

The authors develop a functional linear model in which the values at time t of a sample of curves y(i) (t) are explained in a feed-forward sense by the values of covariate curves x(i) (s) observed at times s less than or equal to t. They give special attention to the case s is an element of [t - delta, t], where the lag parameter delta is estimated from the data. They use the finite element method to estimate the bivariate parameter regression function beta(s, t), which is defined on the triangular domain s less than or equal to t. They apply their model to the problem of predicting the acceleration of the lower lip during speech on the basis of electromyographical recordings from a muscle depressing the lip. They also provide simulation results to guide the calibration of the fitting process.