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Normal reference bandwidths for the general order, multivariate kernel density derivative estimator

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  • Henderson, Daniel J.
  • Parmeter, Christopher F.

Abstract

This note derives the general form of the asymptotic approximate mean integrated squared error for the q-variate, νth-order kernel density rth 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

  • 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.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2198-2205
    DOI: 10.1016/j.spl.2012.07.020
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    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, November.
    2. 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.
    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. 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.
    6. 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.
    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.
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    Cited by:

    1. 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.
    2. 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.
    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; 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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