Revisiting fitting monotone polynomials to data

Kevin Murray (), Samuel Müller () and Berwin Turlach ()

Computational Statistics, 2013, vol. 28, issue 5, 1989-2005

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. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Monotone polynomial; Monotone regression (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00180-012-0390-5

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