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A Review and Comparison of Bandwidth Selection Methods for Kernel Regression

Author

Listed:
  • Max Köhler

    (Georg-August-University Göttingen)

  • Anja Schindler

    (Georg-August-University Göttingen)

  • Stefan Sperlich

    (Université de Genéve)

Abstract

Over the last four decades, several methods for selecting the smoothing parameter, generally called 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 we can still see coming up new ones. Given the need of automatic data-driven bandwidth selectors for applied statistics, this review is intended to explain and compare these methods.

Suggested Citation

  • Max Köhler & Anja Schindler & Stefan Sperlich, 2011. "A Review and Comparison of Bandwidth Selection Methods for Kernel Regression," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 95, Courant Research Centre PEG.
    • Handle: RePEc:got:gotcrc:095
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Feluch, W. & Koronacki, J., 1992. "A note on modified cross-validation in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 13(2), pages 143-151, March.
    5. L. Yang & R. Tschernig, 1999. "Multivariate bandwidth selection for local linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 793-815.
    6. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    7. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
    8. Marron, James Stephen & Härdle, Wolfgang, 1986. "Random approximations to some measures of accuracy in nonparametric curve estimation," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 91-113, October.
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    Cited by:

    1. Scholz, Michael & Nielsen, Jens Perch & Sperlich, Stefan, 2015. "Nonparametric prediction of stock returns based on yearly data: The long-term view," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 143-155.
    2. Inés Barbeito & Ricardo Cao & Stefan Sperlich, 2023. "Bandwidth selection for statistical matching and prediction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 418-446, March.
    3. 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.
    4. 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.
    5. 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.
    6. Jan Koláček & Ivana Horová, 2017. "Bandwidth matrix selectors for kernel regression," Computational Statistics, Springer, vol. 32(3), pages 1027-1046, September.
    7. 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.
    8. 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.
    9. Fritz, Marlon, 2019. "Steady state adjusting trends using a data-driven local polynomial regression," Economic Modelling, Elsevier, vol. 83(C), pages 312-325.
    10. 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.
    11. 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.
    12. Olga Y. Savchuk, 2020. "One-sided cross-validation for nonsmooth density functions," Computational Statistics, Springer, vol. 35(3), pages 1253-1272, September.
    13. 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.
    14. 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.

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    More about this item

    Keywords

    Kernel regression estimation; Bandwidth Selection; Plug-in; Cross Validation;
    All these keywords.

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