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A flexible sequential Monte Carlo algorithm for parametric constrained regression

Author

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  • Ng, Kenyon
  • Turlach, Berwin A.
  • Murray, Kevin

Abstract

An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This algorithm is based on Sequential Monte Carlo–SimulatedAnnealing and only relies on an indicator function that assesses whether or not the constraints are fulfilled, thus allowing the enforcement of various complex constraints by specifying an appropriate indicator function without altering other parts of the algorithm. The algorithm is illustrated by fitting rational function and B-spline regression models subject to a monotonicity constraint. An implementation of the algorithm using R is freely available on GitHub.

Suggested Citation

  • Ng, Kenyon & Turlach, Berwin A. & Murray, Kevin, 2019. "A flexible sequential Monte Carlo algorithm for parametric constrained regression," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 13-26.
    • Handle: RePEc:eee:csdana:v:138:y:2019:i:c:p:13-26
    DOI: 10.1016/j.csda.2019.03.011
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    References listed on IDEAS

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    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, 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. Matzkin, Rosa L, 1991. "Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models," Econometrica, Econometric Society, vol. 59(5), pages 1315-1327, September.
    4. Faming Liang & Yichen Cheng & Guang Lin, 2014. "Simulated Stochastic Approximation Annealing for Global Optimization With a Square-Root Cooling Schedule," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 847-863, June.
    5. Wolters, Mark A., 2012. "A particle swarm algorithm with broad applicability in shape-constrained estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2965-2975.
    6. Enlu Zhou & Xi Chen, 2013. "Sequential Monte Carlo simulated annealing," Journal of Global Optimization, Springer, vol. 55(1), pages 101-124, January.
    7. Roberto Andreani & Ellen H. Fukuda & Paulo J. S. Silva, 2013. "A Gauss–Newton Approach for Solving Constrained Optimization Problems Using Differentiable Exact Penalties," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 417-449, February.
    8. Dimitris Fouskakis & David Draper, 2002. "Stochastic Optimization: a Review," International Statistical Review, International Statistical Institute, vol. 70(3), pages 315-349, December.
    9. Hazelton, Martin L. & Turlach, Berwin A., 2011. "Semiparametric regression with shape-constrained penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2871-2879, October.
    10. Kevin Murray & Samuel Müller & Berwin Turlach, 2013. "Revisiting fitting monotone polynomials to data," Computational Statistics, Springer, vol. 28(5), pages 1989-2005, October.
    11. Mary Meyer & Amber Hackstadt & Jennifer Hoeting, 2011. "Bayesian estimation and inference for generalised partial linear models using shape-restricted splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 867-884.
    12. M. Locatelli, 2000. "Simulated Annealing Algorithms for Continuous Global Optimization: Convergence Conditions," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 121-133, January.
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