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Asymptotic normality of a projective estimator of an infinite-dimensional parameter of nonlinear regression

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Ukrainian Mathematical Journal Aims and scope

Abstract

A model of nonlinear regression is studied in infinite-dimensional space. Observation errors are equally distributed and have the identity correlation operator. A projective estimator of a parameter is constructed, and the conditions under which it is true are established. For a parameter that belongs to an ellipsoid in a Hilbert space, we prove that the estimators are asymptotically normal; for this purpose, the representation of the estimator in terms of the Lagrange factor is used and the asymptotics of this factor are studied. An example of the nonparametric estimator of a signal is examined for iterated observations under an additive noise.

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References

  1. A. G. Kukush, “The convergence in distribution of a normalized projective estimator of an infinite-dimensional parameter of linear regression,”Teor. Ver. Mat. Statist., Issue 48, 1–10 (1993).

    Google Scholar 

  2. A. S. Nemirovskii and R. Z. Khas'minskii, “The nonparametric estimation of the functionals of derivatives of a signal observed under white noise,”Probl. Peredachi Inf.,23, No. 3, 27–38. (1987).

    Google Scholar 

  3. R. I. Jennrich, “Asymptotic properties of nonlinear square estimators,”Ann. Math. Stat.,40, No. 2, 633–643 (1969).

    Google Scholar 

  4. A. V. Ivanov,The Theory of Estimation of the Parameters of Nonlinear Regression Models [in Russian], Author's Abstract of the Doctoral Degree Thesis (Physics and Mathematics), Kiev, 1991.

  5. A.G. Kukush, “The convergence in distribution of a normalized estimator of an infinite-dimensional regression parameter,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 11–14 (1988).

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Authors and Affiliations

  1. Kiev University, Kiev

    A. G. Kukush

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  1. A. G. Kukush
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1205–1214, September, 1993.

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Kukush, A.G. Asymptotic normality of a projective estimator of an infinite-dimensional parameter of nonlinear regression. Ukr Math J 45, 1348–1359 (1993). https://doi.org/10.1007/BF01058633

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  • DOI: https://doi.org/10.1007/BF01058633

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