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Regularity, partial regularity, partial information process, for a filtered statistical model
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  • Published: September 1990

Regularity, partial regularity, partial information process, for a filtered statistical model

  • Jean Jacod1 

Probability Theory and Related Fields volume 86, pages 305–335 (1990)Cite this article

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  • 9 Citations

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Summary

We define “partial regularity” for a filtered statistical (semi-parametric) model indexed by θ∈ℝd, as differentiability in a suitable sense of the partial likelihoods associated with a basic processX. Partial regularity turns out to be equivalent to some sort of differentiability in θ of the characteristics ofX. We also prove that regularity of the model implies partial regularity, and we define a “partial information process”, which is smaller than the “complete” information process. We apply these results to obtain a generalization of Cramer-Rao inequality, and to prove that partial likelihood processes are optimal among all quasi-likelihood processes which are stochastic integrals with respect to the basic processX.

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Authors and Affiliations

  1. Laboratoire de Probabilités, Université Pierre et Marie Curie, Tour 56 (3e étage), 4, Place Jussieu, F-75252, Paris Cedex 05, France

    Jean Jacod

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  1. Jean Jacod
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Jacod, J. Regularity, partial regularity, partial information process, for a filtered statistical model. Probab. Th. Rel. Fields 86, 305–335 (1990). https://doi.org/10.1007/BF01208255

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  • Received: 17 July 1989

  • Revised: 25 November 1989

  • Issue Date: September 1990

  • DOI: https://doi.org/10.1007/BF01208255

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Keywords

  • Statistical Model
  • Information Process
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
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