Revisiting fitting monotone polynomials to data

Computational Statistics volume 28, pages1989–2005(2013)Cite this article

Abstract

We revisit Hawkins’ (Comput Stat 9(3):233–247, 1994) algorithm for fitting monotonic polynomials and discuss some practical issues that we encountered using this algorithm, for example when fitting high degree polynomials or situations with a sparse design matrix but multiple observations per \(x\)-value. As an alternative, we describe a new approach to fitting monotone polynomials to data, based on different characterisations of monotone polynomials and using a Levenberg–Marquardt type algorithm. We consider different parameterisations, examine effective starting values for the non-linear algorithms, and discuss some limitations. We illustrate our methodology with examples of simulated and real world data. All algorithms discussed in this paper are available in the R Development Core Team (A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, 2011) package MonoPoly.

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Acknowledgments

We would like to thank the referees and editors for their helpful comments and suggestions. Samuel Müller was supported by a grant from the Australian Research Council (DP110101998).

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Affiliations

  1. School of Mathematics and Statistics, University of Sydney, Carslaw Building (F07), Sydney, NSW, 2006, Australia

    Kevin Murray & Samuel Müller

  2. School of Mathematics and Statistics (M019), University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Kevin Murray & Berwin A. Turlach

  3. Centre for Applied Statistics (M019), University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Kevin Murray & Berwin A. Turlach

Authors
  1. Kevin Murray
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  2. Samuel Müller
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  3. Berwin A. Turlach
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Correspondence to Kevin Murray.

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Murray, K., Müller, S. & Turlach, B.A. Revisiting fitting monotone polynomials to data. Comput Stat 28, 1989–2005 (2013). https://doi.org/10.1007/s00180-012-0390-5

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Keywords

  • Monotone polynomial
  • Monotone regression