Translation invariant statistical experiments with independent increments

  • Alexander Gushchin
  • Nino Kordzakhia
  • Alexander Novikov


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.


Comparison of experiments Convergence of experiments Experiment with independent increments Hellinger integral Lévy process Lévy–Khintchine triplet Pitman estimator Stochastic exponential Translation invariant experiment 

Mathematics Subject Classification

62B20 62E20 62F15 62M99 



For the first author, this study has been funded by the Russian Academic Excellence Project “5-100”. Research of A. Novikov and N. Kordzakhia was supported by ARC Discovery Grant DP150102758.


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Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.Laboratory of Stochastic Analysis and its ApplicationsNational Research University, Higher School of EconomicsMoscowRussia
  3. 3.Macquarie UniversitySydneyAustralia
  4. 4.Department of Mathematical SciencesUniversity of Technology SydneyBroadway, SydneyAustralia

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