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A Greedy Algorithm for Unimodal Kernel Density Estimation by Data Sharpening

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  • Wolters, Mark A.

Abstract

We consider the problem of nonparametric density estimation where estimates are constrained to be unimodal. Though several methods have been proposed to achieve this end, each of them has its own drawbacks and none of them have readily-available computer codes. The approach of Braun and Hall (2001), where a kernel density estimator is modified by data sharpening, is one of the most promising options, but optimization difficulties make it hard to use in practice. This paper presents a new algorithm and MATLAB code for finding good unimodal density estimates under the Braun and Hall scheme. The algorithm uses a greedy, feasibility-preserving strategy to ensure that it always returns a unimodal solution. Compared to the incumbent method of optimization, the greedy method is easier to use, runs faster, and produces solutions of comparable quality. It can also be extended to the bivariate case.

Suggested Citation

  • Wolters, Mark A., 2012. "A Greedy Algorithm for Unimodal Kernel Density Estimation by Data Sharpening," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i06).
    • Handle: RePEc:jss:jstsof:v:047:i06
    DOI: http://hdl.handle.net/10.18637/jss.v047.i06
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    Cited by:

    1. Hassan Doosti & Peter Hall, 2016. "Making a non-parametric density estimator more attractive, and more accurate, by data perturbation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 445-462, March.
    2. Turnbull, Bradley C. & Ghosh, Sujit K., 2014. "Unimodal density estimation using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 13-29.

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