Reproduction capabilities of penalized hyperbolic-polynomial splines

This paper investigates two important analytical properties of hyperbolic polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-splines), were recently introduced by the authors as a generalization of P splines. HB-splines are bell-shaped basis functions consisting of segments made of real exponentials e(alpha x), e(-alpha x) and linear functions multiplied by these exponentials, xe(+alpha x) and xe(-alpha x). Here, we show that these types of penalized splines reproduce functions in the space {e(-alpha x), xe(-alpha x)}, that is they fit exponential data exactly. Moreover, we show that they conserve the first and second 'exponential' moments. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates two important analytical properties of hyperbolic polynomial penalized splines, HP-splines. The authors introduce HP-splines as a generalization of P splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-splines). The study shows that these penalized splines can fit exponential data exactly and preserve the first and second 'exponential' moments.