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Monotone B-Spline Smoothing for a Generalized Linear Model Response

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  • Wei Wang
  • Dylan S. Small

Abstract

Various methods have been proposed for smoothing under the monotonicity constraint. We review the literature and implement an approach of monotone smoothing with B-splines for a generalized linear model response. The approach is expressed as a quadratic programming problem and is easily solved using the statistical software R. In a simulation study, we find that the approach performs better than other approaches with much faster computation time. The approach can also be used for smoothing under other shape constraints or mixed constraints. Supplementary materials of the appendices and R code to implement the developed approach is available online.

Suggested Citation

  • Wei Wang & Dylan S. Small, 2015. "Monotone B-Spline Smoothing for a Generalized Linear Model Response," The American Statistician, Taylor & Francis Journals, vol. 69(1), pages 28-33, February.
    • Handle: RePEc:taf:amstat:v:69:y:2015:i:1:p:28-33
    DOI: 10.1080/00031305.2014.969445
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    References listed on IDEAS

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    1. Dette, Holger & Neumeyer, Natalie & Pilz, Kay F., 2005. "A Note on Nonparametric Estimation of the Effective Dose in Quantal Bioassay," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 503-510, June.
    2. J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    3. Zheng Wang, 2000. "An algorithm for generalized monotonic smoothing," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(4), pages 495-507.
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