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Lower bounds for risk functions in nonparametric estimation problems

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In 1990, I. Ibragimov and R. Khasminskiĭ have established some general minimax lower bounds of risk functions for probability density estimates. Here analogous results are proved for some other nonparametric estimation problems. Bibliography: 6 titles.

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References

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

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  2. I. A. Ibragimov and R. Z. Khasminskiĭ, Statistical Estimation Theory [in Russian], Moscow (1979).

  3. M. A. Lifshits, Gaussian Random Functions [in Russian], Kiev (1995).

  4. .J. Kingman, Poisson Processes [Russian translation], Moscow (2007).

  5. M. Brown, “Discrimination of Poisson processes,” Ann. Math. Statist., 42, 773–776 (1971).

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  6. U. Grenander, Abstract Inference, J. Wiley (1981).

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University, St. Petersburg, Russia

    I. A. Ibragimov

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  1. I. A. Ibragimov
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Correspondence to I. A. Ibragimov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 396, 2011, pp. 102–110.

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Ibragimov, I.A. Lower bounds for risk functions in nonparametric estimation problems. J Math Sci 188, 694–699 (2013). https://doi.org/10.1007/s10958-013-1160-9

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  • DOI: https://doi.org/10.1007/s10958-013-1160-9

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