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A particle swarm algorithm with broad applicability in shape-constrained estimation

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  • Wolters, Mark A.

Abstract

In nonparametric function estimation, the inclusion of shape constraints can confer several advantages, including improved estimation accuracy, reduced sensitivity to smoothing parameters, and control over the qualitative appearance of the estimate. Finding shape-restricted estimates may require solving a difficult optimization problem, however, making these advantages hard to realize. A particle swarm algorithm is proposed to overcome this barrier and expand the possibilities for shape-constrained estimation. The algorithm uses a cooperative search strategy with two swarms, one focused on global exploration and one focused on local exploitation. The new heuristic has the added advantage of being a general tool, applicable without modification to a variety of estimators, constraints, and objective functions. The algorithm is demonstrated on a number of density estimation and regression problems, and the potential for further improvement is discussed. Supplementary materials, including source code, are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2965-2975
    DOI: 10.1016/j.csda.2011.11.009
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    References listed on IDEAS

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    1. Daniel J. Henderson & Christopher F. Parmeter, 2009. "Imposing economic constraints in nonparametric regression: survey, implementation, and extension," Advances in Econometrics, in: Nonparametric Econometric Methods, pages 433-469, Emerald Group Publishing Limited.
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    Cited by:

    1. Morio, Jérôme & Jacquemart, Damien & Balesdent, Mathieu & Marzat, Julien, 2013. "Optimisation of interacting particle systems for rare event estimation," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 117-128.
    2. 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.
    3. Acitas, Sukru & Aladag, Cagdas Hakan & Senoglu, Birdal, 2019. "A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 116-127.

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