Exact asymptotic minimax constants for the estimation of analytical functions in L p |
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| Authors: | Emmanuel Guerre Alexander B. Tsybakov |
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| Affiliation: | (1) Université Paris VI, UPRES-A 7055 CNRS, 4, pl. Jussieu, B.P. 188, F-75252 Paris Cedex 05, France, FR;(2) CREST, Malakoff, France, FR;(3) Institute for Problems of Information Transmission, Moscow, |
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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. Received: 10 December 1996 / Revised version: 14 December 1997 |
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| Keywords: | Mathematics Subject Classification (1991): Primary 62G05 62G020 secondary 62C20. |
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