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Normal Reference Bandwidths for the General Order, Multivariate Kernel Density Derivative Estimator

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

This note derives the general form of the approximate mean integrated squared error for the q-variate, th-order kernel density r th derivative estimator. This formula allows for normal reference rule-of-thumb bandwidths to be derived. We give tables for some of the most common cases in the literature.

Suggested Citation

  • Daniel J. Henderson & Christopher F. Parmeter, 2011. "Normal Reference Bandwidths for the General Order, Multivariate Kernel Density Derivative Estimator," Working Papers 2011-15, University of Miami, Department of Economics.
    • Handle: RePEc:mia:wpaper:2011-15
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    File URL: https://www.herbert.miami.edu/_assets/files/repec/wp2011-15.pdf
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    References listed on IDEAS

    as
    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    2. Henderson, Daniel J. & Parmeter, Christopher F., 2012. "Canonical higher-order kernels for density derivative estimation," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1383-1387.
    3. Tong Li & Isabelle Perrigne & Quang Vuong, 2002. "Structural Estimation of the Affliated Private Value Auction Model," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 171-193, Summer.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    5. Duong, Tarn & Cowling, Arianna & Koch, Inge & Wand, M.P., 2008. "Feature significance for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4225-4242, May.
    6. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    7. 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. 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.
    2. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    3. Christopher F. Parmeter & Valentin Zelenyuk, 2016. "A Bridge Too Far? The State of the Art in Combining the Virtues of Stochastic Frontier Analysis and Data Envelopement Analysis," Working Papers 2016-10, University of Miami, Department of Economics.

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    More about this item

    Keywords

    Derivative Estimation; Smoothing; AMISE;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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