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Canonical kernels for density estimation


  • Marron, J. S.
  • Nolan, D.


The kernel function in density estimation is uniquely determined up to a scale factor. In this paper, we advocate one particular rescaling of a kernel function, called the canonical kernel, because it is the only version which uncouples the problems of choice of kernel and choice of scale factor. This approach is useful for both pictorial comparison of kernel density estimators and for optimal kernel theory.

Suggested Citation

  • Marron, J. S. & Nolan, D., 1988. "Canonical kernels for density estimation," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 195-199, December.
  • Handle: RePEc:eee:stapro:v:7:y:1988:i:3:p:195-199

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    References listed on IDEAS

    1. Panaretos, John & Xekalaki, Evdokia, 1986. "On Generalized Binomial and Multinomial Distributions and Their Relation to Generalized Poisson Distributions," MPRA Paper 6248, University Library of Munich, Germany.
    2. Panaretos, John & Xekalaki, Evdokia, 1986. "The stuttering generalized waring distribution," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 313-318, October.
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    2. Fousekis, Panos & Lazaridis, Panagiotis, 2001. "Food Expenditure Patterns of the Urban and the Rural Households in Greece. A Kernel Regression Analysis," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 2(1), January.
    3. Paul Deheuvels & David Mason, 2004. "General Asymptotic Confidence Bands Based on Kernel-type Function Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 225-277, October.
    4. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2012. "Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 732-740.
    5. Ezcurra, Roberto, 2007. "Is there cross-country convergence in carbon dioxide emissions?," Energy Policy, Elsevier, vol. 35(2), pages 1363-1372, February.
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    7. Camelia Minoiu & Sanjay Reddy, 2008. "Kernel Density Estimation Based on Grouped Data; The Case of Poverty Assessment," IMF Working Papers 08/183, International Monetary Fund.
    8. 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.
    9. Aude Bernard & Martin Bell, 2015. "Smoothing internal migration age profiles for comparative research," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(33), pages 915-948, May.
    10. Gao, H. Oliver & Johnson, Lynn Schooley, 2009. "Methods of analysis for vehicle soak time data," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(8), pages 744-754, October.
    11. Duong, Tarn, 2015. "Spherically symmetric multivariate beta family kernels," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 141-145.
    12. Maria Grith & Wolfgang Karl Härdle & Melanie Schienle, 2010. "Nonparametric Estimation of Risk-Neutral Densities," SFB 649 Discussion Papers SFB649DP2010-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Härdle, Wolfgang & Müller, Marlene, 1997. "Multivariate and semiparametric kernel regression," SFB 373 Discussion Papers 1997,26, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    14. Camelia Minoiu & Sanjay Reddy, 2014. "Kernel density estimation on grouped data: the case of poverty assessment," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(2), pages 163-189, June.
    15. Giorgio Canarella & Stephen Pollard, 2006. "Distribution dynamics and convergence in Latin America: A non-parametric analysis," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 53(1), pages 68-95, March.
    16. Gatfaoui, Hayette, 2013. "Translating financial integration into correlation risk: A weekly reporting's viewpoint for the volatility behavior of stock markets," Economic Modelling, Elsevier, vol. 30(C), pages 776-791.
    17. Delaigle, Aurore & Hall, Peter, 2006. "On optimal kernel choice for deconvolution," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1594-1602, September.


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