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Asymptotic Normality of Kernel-Type Deconvolution Estimators

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  • BERT VAN ES
  • HAE-WON UH
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    Abstract

    We derive asymptotic normality of kernel-type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider so-called super smooth deconvolution problems where the characteristic function of the known distribution decreases exponentially, but faster than that of the Cauchy distribution. It turns out that the limit behaviour of the pointwise estimators of the density and distribution function is relatively straightforward, while the asymptotic behaviour of the estimator of the probability of an interval depends in a complicated way on the sequence of bandwidths. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..

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    Bibliographic Info

    Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

    Volume (Year): 32 (2005)
    Issue (Month): 3 ()
    Pages: 467-483

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    Handle: RePEc:bla:scjsta:v:32:y:2005:i:3:p:467-483

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    Cited by:
    1. van Es, Bert & Gugushvili, Shota, 2008. "Weak convergence of the supremum distance for supersmooth kernel deconvolution," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(17), pages 2932-2938, December.
    2. Jakob Söhl & Mathias Trabs, 2012. "We estimate linear functionals in the classical deconvolution problem by kernel estimators," SFB 649 Discussion Papers SFB649DP2012-046, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Bissantz, Nicolai & Dümbgen, Lutz & Holzmann, Hajo & Munk, Axel, 2007. "Nonparametric confidence bands in deconvolution density estimation," Technical Reports 2007,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Mynbaev, Kairat, 2011. "Distributions escaping to infinity and the limiting power of the Cliff-Ord test for autocorrelation," MPRA Paper 44402, University Library of Munich, Germany, revised 18 Sep 2012.

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