Sharpening P-spline signal regression

We propose two variations of P-spline signal regression: space-varying penalization signal regression (SPSR) and additive polynomial signal regression (APSR). SPSR uses space-varying roughness penalty according to the estimated coefficients from the partial least-squares (PLS) regression, while APSR expands the linear basis to polynomial bases. SPSR and APSR are motivated in the following two scenarios, respectively: (i) some region(s) of the regressor channels contain more useful information for prediction than others and (ii) the relationship between the response and regressor channels is highly nonlinear. We also extend the methods to the generalized linear regression setting. As illustration, we apply the methods to two published data sets showing highly competitive performance.