Generalized Linear Regression on Sampled Signals and Curves: A P-Spline Approach

We consider generalized linear regression with many highly correlated regressors—for instance, digitized points of a curve on a spatial or temporal domain. We refer to this setting as signal regression, which requires severe regularization because the number of regressors is large, often exceeding the 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 splines. A difference penalty between the B-spline coefficients further increases smoothness-the P-spline framework of Eilers and Marx. The procedure is regulated by a penalty parameter chosen using information criteria or cross-validation.