Revisiting fitting monotone polynomials to data |
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Authors: | Kevin Murray Samuel Müller Berwin A Turlach |
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Institution: | 1. School of Mathematics and Statistics, University of Sydney, Carslaw Building (F07), Sydney, NSW, 2006, Australia 2. School of Mathematics and Statistics (M019), University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia 3. Centre for Applied Statistics (M019), University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia
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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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