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On the Accuracy of Binned Kernel Density Estimators

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  • Hall, Peter
  • Wand, M. P.
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    Abstract

    The accuracy of the binned kernel density estimator is studied for general binning rules. We derive mean squared error results for the closeness of this estimator to both the true density and the unbinned kernel estimator. The binning rule and smoothness of the kernel function are shown to influence the accuracy of the binned kernel estimators. Our results are used to compare commonly used binning rules, and to determine the minimum grid size required to obtain a given level of accuracy.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 56 (1996)
    Issue (Month): 2 (February)
    Pages: 165-184

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    Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:165-184

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    Related research

    Keywords: Binning rules Euler-Maclaurin summation formulae (null);

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    Cited by:
    1. Jan G. de Gooijer & Ao Yuan, 2011. "Kernel-Smoothed Conditional Quantiles of Correlated Bivariate Discrete Data," Tinbergen Institute Discussion Papers 11-011/4, Tinbergen Institute.
    2. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
    3. Meintanis, S. & Ushakov, N. G., 2004. "Binned goodness-of-fit tests based on the empirical characteristic function," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 305-314, September.
    4. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    5. Gonzalez-Manteiga, W. & Sanchez-Sellero, C. & Wand, M. P., 1996. "Accuracy of binned kernel functional approximations," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 1-16, June.
    6. Holmström, Lasse, 2000. "The Accuracy and the Computational Complexity of a Multivariate Binned Kernel Density Estimator," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 264-309, February.
    7. Koo, Ja-Yong & Kooperberg, Charles, 2000. "Logspline density estimation for binned data," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 133-147, January.
    8. Hegland, Markus & McIntosh, Ian & Turlach, Berwin A., 1999. "A parallel solver for generalised additive models," Computational Statistics & Data Analysis, Elsevier, vol. 31(4), pages 377-396, October.
    9. Ignacio García-Jurado, 2008. "Comments on: Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(1), pages 51-53, July.
    10. Kozek, A. S. & Yin, J., 2004. "On Gauss quadrature and partial cross validation," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 431-448, April.

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