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Asymptotic Normality of Kernel-Type Deconvolution Estimators

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  • BERT VAN ES
  • HAE-WON UH

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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  • Bert Van Es & Hae-Won Uh, 2005. "Asymptotic Normality of Kernel-Type Deconvolution Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 467-483.
  • Handle: RePEc:bla:scjsta:v:32:y:2005:i:3:p:467-483
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    Cited by:

    1. Karun Adusumilli & Taisuke Otsu & Yoon-Jae Whang, 2017. "Inference on distribution functions under measurement error," STICERD - Econometrics Paper Series 594, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. van Es, Bert & Gugushvili, Shota, 2008. "Weak convergence of the supremum distance for supersmooth kernel deconvolution," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2932-2938, December.
    3. Peter Hall & Tapabrata Maiti, 2008. "Non-parametric inference for clustered binary and count data when only summary information is available," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 725-738.
    4. 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.
    5. 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.
    6. Mynbaev, Kairat & Martins-Filho, Carlos, 2015. "Consistency and asymptotic normality for a nonparametric prediction under measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 166-188.
    7. 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.
    8. Taisuke Otsu & Luke Taylor, 2016. "Specification testing for errors-in-variables models," STICERD - Econometrics Paper Series /2015/586, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Yang Zu, 2015. "A Note on the Asymptotic Normality of the Kernel Deconvolution Density Estimator with Logarithmic Chi-Square Noise," Econometrics, MDPI, Open Access Journal, vol. 3(3), pages 1-16, July.
    10. Martin L. Hazelton & Berwin A. Turlach, 2010. "Semiparametric Density Deconvolution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 91-108.

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