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Canonical kernels for density estimation

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  • Marron, J. S.
  • Nolan, D.
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 7 (1988)
    Issue (Month): 3 (December)
    Pages: 195-199

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    Handle: RePEc:eee:stapro:v:7:y:1988:i:3:p:195-199

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    Related research

    Keywords: canonical kernels density estimation optimal kernels smoothing;

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    Cited by:
    1. Giorgio Canarella & Stephen Pollard, 2006. "Distribution dynamics and convergence in Latin America: A non-parametric analysis," International Review of Economics, Springer, vol. 53(1), pages 68-95, March.
    2. Shuowen Hu & D.S. Poskitt & Xibin Zhang, 2010. "Bayesian Adaptive Bandwidth Kernel Density Estimation of Irregular Multivariate Distributions," Monash Econometrics and Business Statistics Working Papers 21/10, Monash University, Department of Econometrics and Business Statistics.
    3. 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.
    4. Ezcurra, Roberto, 2007. "Is there cross-country convergence in carbon dioxide emissions?," Energy Policy, Elsevier, vol. 35(2), pages 1363-1372, February.
    5. 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.
    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, vol. 97(4), pages 403-433, October.
    7. 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.
    8. Delaigle, Aurore & Hall, Peter, 2006. "On optimal kernel choice for deconvolution," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1594-1602, September.
    9. 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.
    10. 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.
    11. Ezcurra, Roberto, 2007. "Distribution dynamics of energy intensities: A cross-country analysis," Energy Policy, Elsevier, vol. 35(10), pages 5254-5259, October.
    12. Camelia Minoiu & Sanjay Reddy, 2014. "Kernel density estimation on grouped data: the case of poverty assessment," Journal of Economic Inequality, Springer, vol. 12(2), pages 163-189, June.
    13. M. M. Salinas-Jimenez, 2003. "Technological change, efficiency gains and capital accumulation in labour productivity growth and convergence: an application to the Spanish regions," Applied Economics, Taylor & Francis Journals, vol. 35(17), pages 1839-1851.
    14. Camelia Minoiu & Sanjay Reddy, 2008. "Kernel Density Estimation Basedon Grouped Data," IMF Working Papers 08/183, International Monetary Fund.

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