Penalized hyperbolic-polynomial splines. (August 2021)

• Record Type: Journal Article
• Authors: Campagna, Rosanna; Conti, Costanza
• Is Part Of: Applied mathematics letters. Volume 118(2021)
• Publication Date: 2021-08
• Subjects: Penalized splines -- Discrete penalty -- P-splines -- Hyperbolic-polynomial splines -- B-splines; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107159
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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 α x where r = 0, …, ℓ and α ∈ R . HP-splines, that reduce to P-splines for α = 0, are more suitable to data with an exponential trend which is frequent in applications.