Penalized hyperbolic-polynomial splines

With the aim of generalizing P-splines, we here define a special type of penalized splines, called HP-splines, where polynomial splines are replaced by the richer class of hyperbolic-polynomial splines and a suitably tailored discrete penalty term is used. Hyperbolic-polynomial splines, important in several applications, are a natural generalization of polynomial splines consisting of piecewise-defined functions with segments spanned by 'atoms' of type x(r)e(alpha x) where r = 0, ... , l and alpha is an element of R. HP-splines, that reduce to P-splines for alpha = 0, are more suitable to data with an exponential trend which is frequent in applications. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

HP-splines are a special type of penalized splines that use hyperbolic-polynomial splines instead of polynomial splines, with a tailored discrete penalty term. They are more suitable for data with exponential trends.