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Canonical Higher-Order Kernels for Density Derivative Estimation

Author

Listed:
  • Daniel J. Henderson

    (Department of Economics, State University of New York at Binghamton)

  • Christopher F. Parmeter

    (Department of Economics, University of Miami)

Abstract

In this note we present r th order kernel density derivative estimators using canonical higher-order kernels. These canonical rescalings uncouple the choice of kernel and scale factor. This approach is useful for selection of the order of the kernel in a data-driven procedure as well as for visual comparison of kernel estimates.

Suggested Citation

  • Daniel J. Henderson & Christopher F. Parmeter, 2010. "Canonical Higher-Order Kernels for Density Derivative Estimation," Working Papers 2011-14, University of Miami, Department of Economics.
    • Handle: RePEc:mia:wpaper:2011-14
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    File URL: https://www.herbert.miami.edu/_assets/files/repec/wp2011-14.pdf
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    References listed on IDEAS

    as
    1. Kairat Mynbaev & Carlos Martins-Filho, 2010. "Bias reduction in kernel density estimation via Lipschitz condition," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 219-235.
    2. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    3. Hansen, Bruce E., 2005. "Exact Mean Integrated Squared Error Of Higher Order Kernel Estimators," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1031-1057, December.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Kairat Mynbaev & Carlos Martins-Filho & Aziza Aipenova, 2016. "A Class of Nonparametric Density Derivative Estimators Based on Global Lipschitz Conditions," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 591-615, Emerald Group Publishing Limited.
    2. Henderson, Daniel J. & Parmeter, Christopher F., 2012. "Normal reference bandwidths for the general order, multivariate kernel density derivative estimator," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2198-2205.
    3. Salim Bouzebda & Mohamed Chaouch & Sultana Didi Biha, 2022. "Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 737-771, August.

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    More about this item

    Keywords

    Derivative Estimation; AMISE;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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