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Risk bounds in estimation of symmetrical distributions

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Abstract

We consider a modification of nonparametric informational inequalities derived in [1] using additional information on the infinite-dimensional parameter being estimated. The general constructions are motivated, in particular, by problems of estimation of distribution functions invariant under various transformation groups in ℝk.

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Literature cited

  1. B. Ya. Levit, “Infinite-dimensional information inequalities,” Teor. Veroyatn, Primen.23, No. 2, 388–394 (1978).

    Google Scholar 

  2. V. N. Sudakov, “Geometrical problems in the theory of infinite-dimensional probability distributions,” Tr. Mat. Inst. Akad. Nauk SSSR,61, Nauka, Leningrad (1976).

    Google Scholar 

  3. Yu. A. Koshevnik and B. Ya. Levit, “On lower bounds of risk for nonparametric estimators of distribution functions,” in: Proc. VII Soviet Conf. on Coding Theory and Information Transmission [in Russian], Part 1, Moscow-Vilnius (1978), pp. 80–84.

  4. Yu. A. Koshevnik and B. Ya. Levit, “On a nonparametric analog of the information matrix,” Teor. Veroyatn. Primen.,21, No. 4, 759–774 (1976).

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  5. I. A. Ibragimov and R. Z. Khas'minskii, “Local asymptotic normality for nonidentically distributed observations,” Teor. Veroyatn. Primen.,20, No. 2, 251–266 (1975).

    Google Scholar 

  6. Yu. A. Koshevnik, “On asymptotic distribution of nonparametric estimators of distribution functions under conditions of symmetry,” in: Statistical Methods. Interuniversity Collection [in Russian], Perm State Univ., Perm (1978), pp. 39–57.

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  7. Yu. G. Dmitriev, “On the properties of estimators of distribution functions and functionals with additional prior information,” in: Mathematical Statistics and Its Applications [in Russian], No. 4, Tomsk State Univ. (1976), pp. 63–76.

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Authors
  1. Yu. A. Koshevnik
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  2. B. Ya. Levit
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 98, pp. 98–114, 1980.

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Koshevnik, Y.A., Levit, B.Y. Risk bounds in estimation of symmetrical distributions. J Math Sci 21, 65–75 (1983). https://doi.org/10.1007/BF01091457

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  • DOI: https://doi.org/10.1007/BF01091457

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