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Hilbert space methods in classical problems of mathematical statistics

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Part of the Lecture Notes in Mathematics book series (LNM,volume 550)

Keywords

  • Measurable Space
  • Fisher Information
  • Asymptotic Normality
  • Unbiased Estimator
  • Factorization Theorem

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References

  1. Chernoff H., Sequential analysis and optimal design, Philadelphia, SIAM, 1972.

    CrossRef  MATH  Google Scholar 

  2. Gerlein O.V. and Kagan A.M., Hilbert space methods in classical problems of mathematical statistics (in Russian), Zapiski nauchnyh seminarov Leningrad.otdel enija Matemat. Instituta, Vol. 53(1975), 64–100.

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  3. Bahadur R.R., Sufficiency and statistical decision functions, Ann. Math. Stat., 25,3 (1954), 423–462.

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  4. Halmos P. and Savage L., Application of the Radom-Nikodym theorem to the theory of sufficient statistics, Ann. Math. Stat., 20,2(1949), 225–241.

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  5. Kagan, A.M., Klebanov L.B. and Fintushal S.M., Asymptotic behaviour of the polynomial Pitman estimators (in Russian), Zapiski nauchnyh seminarov Leningrad. otdeleniya Matemat. Instituta, Vol. 43(1974), 30–39

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  6. Cramér H., Mathematical methods of statistics, Princeton Univ. Press, 1946.

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  7. Shenton L.R., Maximum likelihood and efficiency of the method of moments, Biometrika, 37,I,(1950), III–II6.

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  8. Shenton L.R., Moment estimators and maximum likelihood, Biometrika, 45,3,(1958), 311–320.

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© 1976 Springer-Verlag

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Gerlein, O.V., Kagan, A.M. (1976). Hilbert space methods in classical problems of mathematical statistics. In: Maruyama, G., Prokhorov, J.V. (eds) Proceedings of the Third Japan — USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 550. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077488

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  • DOI: https://doi.org/10.1007/BFb0077488

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07995-8

  • Online ISBN: 978-3-540-37966-9

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