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Limit theorems for conditional distributions with regard for large deviations

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Abstract

Possible limit laws are studied for the multivariate conditional distribution of a subset of components of the sum of independent identically distributed random vectors under the condition that other components belong to the domain of large deviations. It is assumed that the considered distribution is absolutely continuous and belongs to the domain of attraction of the normal law but possesses “heavy tails.” The approach suggested is based on the local theorem for large deviations.

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References

  1. V. S. Korolyuk, N. I. Portenko, A. V. Skorokhod, and A. F. Turbin,Handbook on Probability Theory and Mathematical Statistics [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  2. B. Von Bahr, “Multi-dimensional integral limit theorems for large deviations,”Ark. Mat. 7, 89–99 (1967).

    Article  MATH  MathSciNet  Google Scholar 

  3. A. A. Borovkov and B. A. Rogozin, “Central limit theorem in the multidimensional case,”Teor. Veroyatn. Primen.,10, No. 1, 61–69 (1965).

    MATH  MathSciNet  Google Scholar 

  4. A. A. Borovkov and A. A. Mogul’skii, “Large deviations and the test of the statistical hypothesis. I. Large deviations of sums of random vectors,”Sib. Mat. Zh.,2, No. 3, 52–120 (1992).

    MathSciNet  Google Scholar 

  5. P. Ney, “Dominating points and the asymptotics of large deviations for random walk onR d”Ann. Probab.,11, No. 1, 158–167 (1983).

    MATH  MathSciNet  Google Scholar 

  6. L. V. Osipov, “On large deviations for sums of random vectors inR k”J. Multivar. Anal.,11, No. 2, 115–126 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  7. L. V. Rozovskii, “On probabilities of large deviations in some classes ofk-dimensional Borel sets,”J. Multivar. Anal.,17, No. 1, 1–26 (1985).

    Article  MathSciNet  Google Scholar 

  8. A. V. Nagaev, “Limit theorems considering large deviations under a violation of the Cramer condition,”Izv. Akad. Nauk Uz. SSR,6, 17–22 (1969).

    MathSciNet  Google Scholar 

  9. A. V. Nagaev, “Limit theorems for sample coefficients of asymmetry and excess,”Dokl. Akad. Nauk SSSR 198, No. 2, 291–292 (1971).

    MathSciNet  Google Scholar 

  10. K. M. Mukhamedzhanov and A. V. Nagaev, “Limit theorems for conditional distributions,” in:Asymptotic Problems in Probability Theory and Mathematical Statistics [in Russian], Fan, Tashkent (1990), pp. 56–69.

    Google Scholar 

  11. A. V. Nagaev and A. Yu. Zaigraev, “Multidimensional limit theorems allowing large deviations for densities of regular variation,”J. Multivar. Anal. 67, 385–397 (1998).

    Article  MATH  MathSciNet  Google Scholar 

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Authors
  1. A. Yu. Zaigraev
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev; Kopernik Institute, Torun, Poland. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 8, pp. 1054–1064, August, 1999.

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Zaigraev, A.Y. Limit theorems for conditional distributions with regard for large deviations. Ukr Math J 51, 1188–1200 (1999). https://doi.org/10.1007/BF02592507

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  • DOI: https://doi.org/10.1007/BF02592507

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