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Asymptotics for TAYLEX and SIMEX estimators in deconvolution of densities

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  • Christian Wagner
  • Ulrich Stadtmüller

Abstract

We deal with deconvolution problems in density estimation. Assume that the data follow a density, which is a convolution of the original density f being of interest with a noise density fϵ. In order to estimate the density f, one usually should know fϵ completely and then uses some technique for deconvolution. In contrast, the so-called TAYLEX and SIMEX methods introduced by Carroll and Hall and Cook and Stefanski, respectively use partial information on fϵ only and correct the naive density estimator towards the deconvoluted one. In the present paper, we assume that we have more and more information on the noise density when the sample size increases. We show that by applying these methods, one can achieve almost optimal rates and optimal rates respectively for densities f belonging to certain Sobolev classes.

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  • Christian Wagner & Ulrich Stadtmüller, 2008. "Asymptotics for TAYLEX and SIMEX estimators in deconvolution of densities," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 507-522.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:6:p:507-522
    DOI: 10.1080/10485250802051064
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    1. Bissantz, Nicolai & Hohage, T. & Munk, Axel & Ruymgaart, F., 2007. "Convergence rates of general regularization methods for statistical inverse problems and applications," Technical Reports 2007,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Julie McIntyre & Ronald P. Barry, 2012. "Bivariate deconvolution with SIMEX: an application to mapping Alaska earthquake density," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 297-308, April.

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