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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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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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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DOI: https://doi.org/10.1007/s00180-012-0390-5