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On asymptotic normality of the least square estimators of an infinite-dimensional parameter

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Asymptotic properties of the estimators of an infinite-dimensional parameter are studied.

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References

  1. R. I. Jennrich, “Asymptotic properties of nonlinear squares estimators,”Ann. Math. Statist.,98, No. 2 (1969).

    Google Scholar 

  2. A. Ya. Dorogovtsev,Theory of Estimators of Parameters of Random Processes [in Russian], Vyshcha Shkola, Kiev (1982).

    Google Scholar 

  3. H. Lauter, “Note on the strong consistency of the least squares estimator in nonlinear regression,”Statistics,20, No. 2, 199–210 (1989).

    Google Scholar 

  4. G. Kramer,Mathematical Methods of Statistics [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  5. A. Ya. Dorogovtsev, N. Zerek, and A. G. Kukush, “Asymptotic properties of nonlinear regression estimators in Hilbert space,”Theor. Probab. Math. Statist., No. 35, 37–44 (1987) (English transi, AMS, 1987).

    Google Scholar 

  6. A. Ya. Dorogovtsev, N. Zerek, and A. G. Kukush, “Weak convergence of an infinite-dimensional parameter to a normal distribution,” Ibid., No. 37, 45–51 (1987) (English transi., AMS, 1988).

    Google Scholar 

  7. J. -P. Aubin and I. Ekeland,Applied Nonlinear Analysis, Wiley, New York (1984).

    Google Scholar 

  8. L. A. Lyusternik and V. I. Sobolev,Brief Course of Functional Analysis [in Russian], Vysshaya Shkola, Moscow (1982).

    Google Scholar 

  9. A. I. Arkin and I. V. Evstigneev,Probability Models of Control and Economical Dynamics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  10. V. Hildenbrand,Nuclear and Equilibrium in Big Economic [Russian translation], Nauka, Moscow (1986).

    Google Scholar 

  11. A. Ya. Dorogovtsev, “Consistency of least squares estimators of infinite-dimensional parameter,”Sib. Mat. Zh.,33, No. 4, 65–69 (1992).

    Google Scholar 

  12. K. Iosida,Functional Analysis [Russian translation], Mir, Moscow (1967).

    Google Scholar 

  13. A. Kartan,Differential Calculus. Differential Forms [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  14. A. Araujo and E. Gine,The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York (1980).

    Google Scholar 

  15. N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan,Probability Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 44–53, January, 1993.

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Dorogovtsev, A.Y. On asymptotic normality of the least square estimators of an infinite-dimensional parameter. Ukr Math J 45, 48–58 (1993). https://doi.org/10.1007/BF01062037

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  • DOI: https://doi.org/10.1007/BF01062037

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