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Nonparametric estimation of level sets under minimal assumptions

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  • Ren, Qunshu
  • Mojirsheibani, Majid

Abstract

Baillo et al. [Baillo, A., Cuesta-Albertos, J.A., Cuevas, A., 2001. Convergence rates in nonparametric estimation of level sets. Statist. Probab. Lett. 53, 27-35] established L1-convergence results for nonparametric estimators of level sets, for i.i.d. sequences, under a highly technical assumption imposed on the underlying density function. In this article we establish the same results (with the same rates of convergence) without imposing such technical conditions. Furthermore, the i.i.d. assumption used in the cited paper will be relaxed to the one based on [alpha]-mixing sequences. We require no additional conditions to establish our results.

Suggested Citation

  • Ren, Qunshu & Mojirsheibani, Majid, 2008. "Nonparametric estimation of level sets under minimal assumptions," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3029-3033, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:3029-3033
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    References listed on IDEAS

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    1. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.
    2. Polonik, Wolfgang, 1997. "Minimum volume sets and generalized quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 1-24, July.
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    Cited by:

    1. Delicado, Pedro & Vieu, Philippe, 2015. "Optimal level sets for bivariate density representation," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 1-18.

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