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A class of nonparametric density derivative estimators based on global Lipschitz conditions

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  • Mynbaev, Kairat
  • Martins-Filho, Carlos
  • Aipenova, Aziza

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

  • Mynbaev, Kairat & Martins-Filho, Carlos & Aipenova, Aziza, 2015. "A class of nonparametric density derivative estimators based on global Lipschitz conditions," MPRA Paper 75909, University Library of Munich, Germany, revised 2014.
    • Handle: RePEc:pra:mprapa:75909
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    File URL: https://mpra.ub.uni-muenchen.de/75909/1/MPRA_paper_75909.pdf
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    References listed on IDEAS

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    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. 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. 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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    1. Kairat Mynbaev & Carlos Martins-Filho, 2019. "Unified estimation of densities on bounded and unbounded domains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 853-887, August.

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    More about this item

    Keywords

    nonparametric derivative estimation; Lipschitz conditions;

    JEL classification:

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

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