Fast and flexible methods for monotone polynomial fitting

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Authors Kevin Murray, Samuel Mueller, Berwin A. Turlach
Journal/Conference Name Journal of Statistical Computation and Simulation
Paper Category
Paper Abstract ABSTRACTWe investigate an isotonic parameterization for monotone polynomials previously unconsidered in the statistical literature. We show that this parameterization is more flexible than its alternatives through enabling polynomials to be constrained to be monotone over either a compact interval or a semi-compact interval of the form [a,āˆž), in addition to over the whole real line. Furthermore, algorithms based on our new parameterization estimate the fitted monotone polynomials much faster than algorithms based on previous isotonic parameterizations which in turn makes the use of standard bootstrap methodology feasible. We investigate the use of the bootstrap under monotonicity constraints to obtain confidence bands for the fitted curves and show that an adjustment by using either the ā€˜m out of nā€™ bootstrap or a post hoc symmetrization of the confidence bands is necessary to achieve more uniform coverage probabilities. We illustrate our new methodology with two real world examples which demonstrate not ...
Date of publication 2016
Code Programming Language R

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