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Robust Estimators under the Imprecise Dirichlet Model


Author: Marcus Hutter (2002-2003)
Comments: 16 pages
Subj-class: Probability Theory
Reference: Proceedings of the 3rd International Symposium on Imprecise Probabilities and Their Applications (ISIPTA 2003) pages 274-289
Report-no: IDSIA-03-03 and math.PR/0305121
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Extended Paper:

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Slides: PostScript - PDF

Keywords: Imprecise Dirichlet Model; exact, conservative, approximate, robust, credible interval estimates; entropy; mutual information.

Abstract: Walley's Imprecise Dirichlet Model (IDM) for categorical data overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or intervals. The main objective of this work is to derive exact, conservative, and approximate, robust and credible interval estimates under the IDM for a large class of statistical estimators, including the entropy and mutual information.

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BibTeX Entry

@InProceedings{Hutter:03idm,
  author =       "M. Hutter",
  number =       "IDSIA-03-03",
  title =        "Robust Estimators under the {I}mprecise {D}irichlet {M}odel",
  booktitle =    "Proceedings of the 3nd International Symposium on
                  Imprecise Probabilities and Their Application ({ISIPTA-2003})",
  editor =       "J.-M. Bernard and T. Seidenfeld and M. Zaffalon",
  publisher =    "Carleton Scientific",
  series =       "Proceedings in Informatics",
  volume =       "18",
  address =      "Canada",
  year =         "2003",
  pages =        "274--289",
  http =         "http://www.hutter1.net/ai/idm.htm",
  url =          "http://arxiv.org/abs/math.PR/0305121",
  ftp =          "ftp://ftp.idsia.ch/pub/techrep/IDSIA-03-03.ps.gz",
  keywords =     "Imprecise Dirichlet Model; exact, conservative, approximate,
                  robust, confidence interval estimates; entropy; mutual information.",
  abstract =     "Walley's Imprecise Dirichlet Model (IDM) for categorical data
                  overcomes several fundamental problems which other approaches to
                  uncertainty suffer from. Yet, to be useful in practice, one needs
                  efficient ways for computing the imprecise=robust sets or
                  intervals. The main objective of this work is to derive exact,
                  conservative, and approximate, robust and credible interval
                  estimates under the IDM for a large class of statistical
                  estimators, including the entropy and mutual information.",
}
      
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