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A general result on the uniform in bandwidth consistency of kernel-type function estimators

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An Erratum to this article was published on 25 November 2014

Abstract

We develop a general theorem to prove the uniform in bandwidth consistency of kernel-type function estimators. This method unifies the approaches in some other recent papers. We show how to apply our results to kernel distribution function estimators and the smoothed empirical process. The results are applicable to establish strong uniform consistency of data-driven bandwidth kernel-type function estimators.

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Authors and Affiliations

  1. Statistics Program, University of Delaware, Newark, DE, 19716, USA

    David M. Mason

  2. North-West University, Potchefstroom Campus, Potchefstroom, South Africa

    Jan W. H. Swanepoel

Authors
  1. David M. Mason
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  2. Jan W. H. Swanepoel
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Corresponding author

Correspondence to David M. Mason.

Additional information

David M. Mason’s research was partially supported by NSF Grant DMS–0503908 and Jan W.H. Swanepoel’s was partially supported by NRF of South Africa.

An erratum to this article is available at http://dx.doi.org/10.1007/s11749-014-0420-4.

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Mason, D.M., Swanepoel, J.W.H. A general result on the uniform in bandwidth consistency of kernel-type function estimators. TEST 20, 72–94 (2011). https://doi.org/10.1007/s11749-010-0188-0

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  • DOI: https://doi.org/10.1007/s11749-010-0188-0

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