Statistical application of barycentric rational
interpolants : an alternative to splines

Baker, RD; Jackson, D

Abstract

Spline curves, originally developed by numerical analysts for interpolation,
are widely used in statistical work, mainly as regression splines and smoothing
splines. Barycentric rational interpolants have recently been developed by numerical
analysts, but have yet seen very few statistical applications. We give the necesssary
information to enable the reader to use barycentric rational interpolants, including a
suggestion for a Bayesian prior distribution, and explore the possible statistical use
of barycentric interpolants as an alternative to splines. We give the all the necessary
formulae, compare the numerical accuracy to splines for some Monte-Carlo datasets,
and apply both regression splines and barycentric interpolants to two real datasets.We
also discuss the application of these interpolants to data smoothing, where smoothing
splines would normally be used, and exemplify the use of smoothing interpolants
with another real dataset. Our conclusion is that barycentric interpolants are as accurate
as splines, and no more difficult to understand and program. They offer a viable
alternative methodology.

Citation

interpolants : an alternative to splines. Computational Statistics, 29(5), 1065-1081. https://doi.org/10.1007/s00180-014-0480-7

• Journal Article Type: Article
• Acceptance Date: Jan 15, 2014
• Online Publication Date: Feb 4, 2014
• Publication Date: Feb 4, 2014
• Deposit Date: Feb 21, 2014
• Journal: Computational Statistics and Data Analysis
• Print ISSN: 0943-4062
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 5
• Pages: 1065-1081
• DOI: https://doi.org/10.1007/s00180-014-0480-7
• Publisher URL: http://dx.doi.org/10.1007/s00180-014-0480-7
• Related Public URLs: http://link.springer.com/journal/volumesAndIssues/180