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Pointwise and uniform convergence of kernel density estimators using random bandwidths

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  • Dutta, Santanu
  • Goswami, Alok

Abstract

We obtain the rates of pointwise and uniform convergence of kernel density estimators using random bandwidths under i.i.d. as well as strongly mixing dependence assumptions. Pointwise rates are faster and not affected by the tail of the density.

Suggested Citation

  • Dutta, Santanu & Goswami, Alok, 2013. "Pointwise and uniform convergence of kernel density estimators using random bandwidths," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2711-2720.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2711-2720
    DOI: 10.1016/j.spl.2013.09.010
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    References listed on IDEAS

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    1. Wied, Dominik & Weißbach, Rafael, 2010. "Consistency of the kernel density estimator - a survey," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 53(1), pages 1-21.
    2. Mielniczuk, Jan, 1990. "Remark concerning data-dependent bandwidth choice in density estimation," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 27-33, January.
    3. Dominik Wied & Rafael Weißbach, 2012. "Consistency of the kernel density estimator: a survey," Statistical Papers, Springer, vol. 53(1), pages 1-21, February.
    4. Bose, Arup & Dutta, Santanu, 2013. "Density estimation using bootstrap bandwidth selector," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 245-256.
    5. Salim Lardjane, 2007. "Nonparametric density estimation for nonmixing approximable Stochastic Processes," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 209-221, October.
    6. Cao, Ricardo & Cuevas, Antonio & Gonzalez Manteiga, Wensceslao, 1994. "A comparative study of several smoothing methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 153-176, February.
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