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Discrimination distance bounds and statistical applications
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  • Published: September 1990

Discrimination distance bounds and statistical applications

  • Marek Kanter1 

Probability Theory and Related Fields volume 86, pages 403–422 (1990)Cite this article

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Summary

Bounds are obtained for the Kullback-Leibler discrimination distance between two random vectorsX andY. IfX is a sequence of independent random variables whose densities have similar tail behavior andY=AX, whereA is an invertible matrix, then the bounds are a product of terms depending onA andX separately. We apply these bounds to obtain the best possible rate of convergence for any estimator of the parameters of an autoregressive process with innovations in the domain of attraction of a stable law. We provide a general theorem establishing the link between total variation proximity of measures and the rate of convergence of statistical estimates to complete the exposition for this application.

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Authors and Affiliations

  1. 1216 Monterey Avenue, 94707, Berkeley, CA, USA

    Marek Kanter

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  1. Marek Kanter
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Kanter, M. Discrimination distance bounds and statistical applications. Probab. Th. Rel. Fields 86, 403–422 (1990). https://doi.org/10.1007/BF01208258

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  • Received: 02 February 1990

  • Revised: 22 February 1990

  • Issue Date: September 1990

  • DOI: https://doi.org/10.1007/BF01208258

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Keywords

  • Total Variation
  • Stochastic Process
  • Probability Theory
  • Statistical Estimate
  • Mathematical Biology
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