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Exact asymptotic minimax constants for the estimation of analytical functions in L p
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  • Published: September 1998

Exact asymptotic minimax constants for the estimation of analytical functions in L p

  • Emmanuel Guerre1 &
  • Alexander B. Tsybakov1 

Probability Theory and Related Fields volume 112, pages 33–51 (1998)Cite this article

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  • 10 Citations

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Abstract.

The L p minimax risks (1≤p<∞) are studied for statistical estimation in the Gaussian white noise model. The asymptotic rate and constants are given, and the optimal estimator is proposed. This, together with the work of Golubev, Levit and Tsybakov (1996) establishes the classification of the L p minimax constants on the classes of analytical functions.

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  1.  Université Paris VI, UPRES-A 7055 CNRS, 4, pl. Jussieu, B.P. 188, F-75252 Paris Cedex 05, France, , , , , , FR

    Emmanuel Guerre & Alexander B. Tsybakov

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  1. Emmanuel Guerre
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  2. Alexander B. Tsybakov
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Received: 10 December 1996 / Revised version: 14 December 1997

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Guerre, E., Tsybakov, A. Exact asymptotic minimax constants for the estimation of analytical functions in L p . Probab Theory Relat Fields 112, 33–51 (1998). https://doi.org/10.1007/s004400050182

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  • Issue Date: September 1998

  • DOI: https://doi.org/10.1007/s004400050182

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  • Mathematics Subject Classification (1991): Primary 62G05
  • 62G020; secondary 62C20.
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