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Translation invariant statistical experiments with independent increments

Author

Listed:
  • Alexander Gushchin

    (Steklov Mathematical Institute
    National Research University, Higher School of Economics)

  • Nino Kordzakhia

    (Macquarie University)

  • Alexander Novikov

    (University of Technology Sydney)

Abstract

We provide a full description of the class of translation invariant experiments with independent increments. Necessary and sufficient conditions for the weak convergence and the comparison of experiments within this class are given. Finally, we prove exponential boundedness of Pitman estimators in these models.

Suggested Citation

  • Alexander Gushchin & Nino Kordzakhia & Alexander Novikov, 2018. "Translation invariant statistical experiments with independent increments," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 363-383, July.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:2:d:10.1007_s11203-018-9179-7
    DOI: 10.1007/s11203-018-9179-7
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    References listed on IDEAS

    as
    1. Gushchin A. A. & Valkeila Esko, 2003. "Approximations and limit theorems for likelihood ratio processes in the binary case," Statistics & Risk Modeling, De Gruyter, vol. 21(3/2003), pages 219-260, March.
    2. Sergueï Dachian & Ilia Negri, 2011. "On compound Poisson processes arising in change-point type statistical models as limiting likelihood ratios," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 255-271, October.
    3. Janssen, Arnold, 1986. "Limits of translation invariant experiments," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 129-142, October.
    4. Becker C. & Strasser H., 1986. "Local Asymptotic Admissibility Of Pitman Estimates," Statistics & Risk Modeling, De Gruyter, vol. 4(1), pages 61-74, January.
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    Cited by:

    1. Krzysztof Dȩbicki & Enkelejd Hashorva, 2020. "Approximation of Supremum of Max-Stable Stationary Processes & Pickands Constants," Journal of Theoretical Probability, Springer, vol. 33(1), pages 444-464, March.

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