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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.

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Bibliographic Info

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

Volume (Year): 82 (2012)
Issue (Month): 12 ()
Pages: 2198-2205

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Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2198-2205

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Keywords: Derivative estimation; Smoothing; AMISE;

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  1. 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.
  2. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  3. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521586115, October.
  4. Hansen, Bruce E., 2005. "Exact Mean Integrated Squared Error Of Higher Order Kernel Estimators," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1031-1057, December.
  5. 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.
  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.
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