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On the Accuracy of Binned Kernel Density Estimators

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  • Hall, Peter
  • Wand, M. P.

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.

Suggested Citation

  • Hall, Peter & Wand, M. P., 1996. "On the Accuracy of Binned Kernel Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 165-184, February.
    • Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:165-184
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    Citations

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    Cited by:

    1. Liu, Yang & Ruppert, David, 2021. "Density estimation on a network," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. Koo, Ja-Yong & Kooperberg, Charles, 2000. "Logspline density estimation for binned data," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 133-147, January.
    3. 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.
    4. 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.
    5. Tang, Qingguo & Karunamuni, Rohana J., 2016. "Fast and accurate computation for kernel estimators," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 49-62.
    6. 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.
    7. Michel Harel & Jean-François Lenain & Joseph Ngatchou-Wandji, 2016. "Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 296-321, June.
    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. Miguel Reyes & Mario Francisco-Fernández & Ricardo Cao, 2017. "Bandwidth selection in kernel density estimation for interval-grouped data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 527-545, September.
    10. Slone, D.H., 2011. "Increasing accuracy of dispersal kernels in grid-based population models," Ecological Modelling, Elsevier, vol. 222(3), pages 573-579.
    11. Gao, Wenwu & Wang, Jiecheng & Zhang, Ran, 2023. "Quasi-interpolation for multivariate density estimation on bounded domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 592-608.
    12. Walter, Paul & Weimer, Katja, 2018. "Estimating poverty and inequality indicators using interval censored income data from the German microcensus," Discussion Papers 2018/10, Free University Berlin, School of Business & Economics.
    13. Jiecheng Wang & Yantong Liu & Jincai Chang, 2022. "An Improved Model for Kernel Density Estimation Based on Quadtree and Quasi-Interpolation," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    14. 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.
    15. 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.
    16. 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.
    17. 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;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 51-53, July.
    18. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
    19. M. P. Wand & J. C. F. Yu, 2022. "Density estimation via Bayesian inference engines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 199-216, June.
    20. Semeyutin, Artur & O’Neill, Robert, 2019. "A brief survey on the choice of parameters for: “Kernel density estimation for time series data”," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).

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