Generalized linear regression on sampled signals and curves: A P-spline approach

We consider generalized linear regression with many highly correlated regre ssors-for instance, digitized points of a curve on a spatial or temporal do main. We refer to this setting as signal regression, which requires severe regularization because the number of regressors is large, often exceeding t he number of observations. We solve collinearity by forcing the coefficient vector to be smooth on the same domain. Dimension reduction is achieved by projecting the signal coefficient vector onto a moderate number of B splin es. A difference penalty between the B-spline coefficients further increase s smoothness-the P-spline framework of filers and Marx. The procedure is re gulated by a penalty parameter chosen using information criteria or cross-v alidation.