The historical functional linear model
Nicole Malfait, J. O. Ramsay · Canadian Journal of Statistics · 2003
Abstract The authors develop a functional linear model in which the values at time t of a sample of curves yi (t) are explained in a feed‐forward sense by the values of covariate curves xi(s) observed at times s ±.t. They give special attention to the case s ± [t — δ, t], where the lag parameter δ is estimated from the data. They use the finite element method to estimate the bivariate parameter regression function β(s, t), which is defined on the triangular domain s ± 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.