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

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  • David Mason

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  • Jan Swanepoel

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. Copyright Sociedad de Estadística e Investigación Operativa 2011

Suggested Citation

  • David Mason & Jan Swanepoel, 2011. "A general result on the uniform in bandwidth consistency of kernel-type function estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 72-94, May.
    • Handle: RePEc:spr:testjl:v:20:y:2011:i:1:p:72-94
    DOI: 10.1007/s11749-010-0188-0
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    References listed on IDEAS

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    1. D. Boos, 1986. "Rates of convergence for the distance between distribution function estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 33(1), pages 197-202, December.
    2. Jan W. H. Swanepoel & Francois C. Van Graan, 2005. "A New Kernel Distribution Function Estimator Based on a Non-parametric Transformation of the Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 551-562.
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    Cited by:

    1. David Mason, 2012. "Proving consistency of non-standard kernel estimators," Statistical Inference for Stochastic Processes, Springer, vol. 15(2), pages 151-176, July.
    2. Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2016. "Bernstein estimation for a copula derivative with application to conditional distribution and regression functionals," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 351-374, June.

    More about this item

    Keywords

    Kernel estimation; Distribution function; Uniform in bandwidth; 60F15; 62G07; 62G08;

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