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We estimate linear functionals in the classical deconvolution problem by kernel estimators

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  • Jakob Söhl
  • Mathias Trabs
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    Abstract

    We obtain a uniform central limit theorem with square root n rate on the assumption that the smoothness of the functionals is larger than the ill-posedness of the problem, which is given by the polynomial decay rate of the characteristic function of the error. The limit distribution is a generalized Brownian bridge with a covariance structure that depends on the characteristic function of the error and on the functionals. The proposed estimators are optimal in the sense of semiparametric efficiency. The class of linear functionals is wide enough to incorporate the estimation of distribution functions. The proofs are based on smoothed empirical processes and mapping properties of the deconvolution operator.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2012-046.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2012-046.

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    Length: 30 pages
    Date of creation: Jul 2012
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    Handle: RePEc:hum:wpaper:sfb649dp2012-046

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    Related research

    Keywords: Deconvolution; Donsker theorem; Efficiency; Distribution function; Smoothed empirical processes; Fourier multiplier;

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    1. 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, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 467-483.
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