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Statistical application of barycentric rational interpolants: an alternative to splines

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  • Rose Baker
  • Dan Jackson

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. Copyright The Author(s) 2014

Suggested Citation

  • Rose Baker & Dan Jackson, 2014. "Statistical application of barycentric rational interpolants: an alternative to splines," Computational Statistics, Springer, vol. 29(5), pages 1065-1081, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:1065-1081
    DOI: 10.1007/s00180-014-0480-7
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    2. Blaž Krese & Erik Štrumbelj, 2021. "A Bayesian approach to time-varying latent strengths in pairwise comparisons," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-17, May.
    3. Baker, Rose D. & McHale, Ian G., 2018. "Time-varying ratings for international football teams," European Journal of Operational Research, Elsevier, vol. 267(2), pages 659-666.

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