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On a Problem of Estimation of Infinite-Dimensional Parameter

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Let X be a random variable taking positive integer values and let P{X = k} = θ(k). We consider the problem of estimation of the parameter θ = (θ(1), θ(2), . . . ) on the base of a sample X1,X2, . . . , Xn, where the observations Xj are independent copies of X. Bibliography: 5 titles.

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References

  1. P. Billingsley, Convergence of Probability Measures [Russian translation], Moscow (1977).

  2. U. Grenander, Abstract Inference, Wiley, New York (1981).

  3. I. A. Ibragimov and R. Z. Hasminskii, Asymptotic Theory of Estimation [in Russian], Moscow (1979).

  4. V. V. Petrov, Limit Theorems for Sums of Independent Random Variables [in Russian], Moscow (1987).

  5. R. Hasminskii and I. Ibragimov, “On density estimation in the view of Kolmogorov’s ideas in approximation theory,” Ann. Statist., 18, 999–1010 (1990).

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Correspondence to I. A. Ibragimov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 441, 2015, pp. 187–203.

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Ershov, V.A., Ibragimov, I.A. On a Problem of Estimation of Infinite-Dimensional Parameter. J Math Sci 219, 731–742 (2016). https://doi.org/10.1007/s10958-016-3142-1

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  • DOI: https://doi.org/10.1007/s10958-016-3142-1

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