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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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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DOI: https://doi.org/10.1007/s004400050182
- Mathematics Subject Classification (1991): Primary 62G05
- 62G020; secondary 62C20.