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A Review and Comparison of Bandwidth Selection Methods for Kernel Regression

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  • Max Köhler
  • Anja Schindler
  • Stefan Sperlich

Abstract

type="main" xml:id="insr12039-abs-0001"> Over the last decades, several methods for selecting the bandwidth have been introduced in kernel regression. They differ quite a bit, and although there already exist more selection methods than for any other regression smoother, one can still observe coming up new ones. Given the need of automatic data-driven bandwidth selectors for applied statistics, this review is intended to explain and, above all, compare these methods. About 20 different selection methods have been revised, implemented and compared in an extensive simulation study.

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  • Max Köhler & Anja Schindler & Stefan Sperlich, 2014. "A Review and Comparison of Bandwidth Selection Methods for Kernel Regression," International Statistical Review, International Statistical Institute, vol. 82(2), pages 243-274, August.
    • Handle: RePEc:bla:istatr:v:82:y:2014:i:2:p:243-274
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    File URL: http://hdl.handle.net/10.1111/insr.12039
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    1. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch & Sperlich, Stefan, 2011. "Do-Validation for Kernel Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 651-660.
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    5. Gonzalez Manteiga, W. & Martinez Miranda, M. D. & Perez Gonzalez, A., 2004. "The choice of smoothing parameter in nonparametric regression through Wild Bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 487-515, October.
    6. Nils-Bastian Heidenreich & Anja Schindler & Stefan Sperlich, 2013. "Bandwidth selection for kernel density estimation: a review of fully automatic selectors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 403-433, October.
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    1. Stefan Sperlich, 2022. "Comments on: hybrid semiparametric Bayesian networks," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 335-339, June.
    2. Jan Koláček & Ivana Horová, 2017. "Bandwidth matrix selectors for kernel regression," Computational Statistics, Springer, vol. 32(3), pages 1027-1046, September.
    3. Olga Y. Savchuk, 2020. "One-sided cross-validation for nonsmooth density functions," Computational Statistics, Springer, vol. 35(3), pages 1253-1272, September.
    4. Fritz, Marlon, 2019. "Steady state adjusting trends using a data-driven local polynomial regression," Economic Modelling, Elsevier, vol. 83(C), pages 312-325.
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    7. Bansal, Prateek & Daziano, Ricardo A. & Sunder, Naveen, 2019. "Arriving at a decision: A semi-parametric approach to institutional birth choice in India," Journal of choice modelling, Elsevier, vol. 31(C), pages 86-103.
    8. Andrea Meilán-Vila & Mario Francisco-Fernández & Rosa M. Crujeiras & Agnese Panzera, 2021. "Nonparametric multiple regression estimation for circular response," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 650-672, September.
    9. José María Sarabia & Faustino Prieto & Vanesa Jordá & Stefan Sperlich, 2020. "A Note on Combining Machine Learning with Statistical Modeling for Financial Data Analysis," Risks, MDPI, vol. 8(2), pages 1-14, April.
    10. Isabel Proença & Stefan Sperlich & Duygu Savaşcı, 2015. "Semi-mixed effects gravity models for bilateral trade," Empirical Economics, Springer, vol. 48(1), pages 361-387, February.
    11. Olga Y. Savchuk & Jeffrey D. Hart, 2017. "Fully robust one-sided cross-validation for regression functions," Computational Statistics, Springer, vol. 32(3), pages 1003-1025, September.
    12. Roland Langrock & Nils-Bastian Heidenreich & Stefan Sperlich, 2014. "Kernel-based semiparametric multinomial logit modelling of political party preferences," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 435-449, August.
    13. Kateřina Konečná & Ivanka Horová, 2019. "Maximum likelihood method for bandwidth selection in kernel conditional density estimate," Computational Statistics, Springer, vol. 34(4), pages 1871-1887, December.
    14. Samuele Tosatto & Riad Akrour & Jan Peters, 2020. "An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions," Stats, MDPI, vol. 4(1), pages 1-17, December.

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