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A Class of Nonparametric Density Derivative Estimators Based on Global Lipschitz Conditions

In: Essays in Honor of Aman Ullah

Author

Listed:
  • Kairat Mynbaev
  • Carlos Martins-Filho
  • Aziza Aipenova

Abstract

Abstract Estimators for derivatives associated with a density function can be useful in identifying its modes and inflection points. In addition, these estimators play an important role in plug-in methods associated with bandwidth selection in nonparametric kernel density estimation. In this paper, we extend the nonparametric class of density estimators proposed by Mynbaev and Martins-Filho (2010) to the estimation of m-order density derivatives. Contrary to some existing derivative estimators, the estimators in our proposed class have a full asymptotic characterization, including uniform consistency and asymptotic normality. An expression for the bandwidth that minimizes an asymptotic approximation for the estimators’ integrated squared error is provided. A Monte Carlo study sheds light on the finite sample performance of our estimators and contrasts it with that of density derivative estimators based on the classical Rosenblatt–Parzen approach.

Suggested Citation

  • 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 Publishing Ltd.
  • Handle: RePEc:eme:aecozz:s0731-905320160000036026
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    References listed on IDEAS

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    1. repec:taf:gnstxx:v:22:y:2010:i:2:p:219-235 is not listed on IDEAS
    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. 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.
    4. Singh, Radhey S., 1987. "Mise of kernel estimates of a density and its derivatives," Statistics & Probability Letters, Elsevier, vol. 5(2), pages 153-159, March.
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    Cited by:

    1. Mynbayev, Kairat & Martins-Filho, Carlos, 2017. "Unified estimation of densities on bounded and unbounded domains," MPRA Paper 87044, University Library of Munich, Germany, revised Jan 2018.

    More about this item

    Keywords

    Nonparametric derivative estimation; Lipschitz conditions; 62G07; 62G20; C14; C18;

    JEL classification:

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

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