Exact asymptotic minimax constants for the estimation of analytical functions in Lp

Emmanuel Guerre; Alexander B. Tsybakov

doi:10.1007/s004400050182

Exact asymptotic minimax constants for the estimation of analytical functions in L_p

Emmanuel Guerre
, Alexander B. Tsybakov

Sorbonne Université
ENSAE
Institute for Information Transmission Problems (RAS)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	33-51
Number of pages	19
Journal	Probability Theory and Related Fields
Volume	112
Issue number	1
DOIs	https://doi.org/10.1007/s004400050182
Publication status	Published - 1 Jan 1998

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title = "Exact asymptotic minimax constants for the estimation of analytical functions in Lp",

abstract = "The Lp, 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 Lp minimax constants on the classes of analytical functions.",

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AB - The Lp, 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 Lp minimax constants on the classes of analytical functions.

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JO - Probability Theory and Related Fields

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Exact asymptotic minimax constants for the estimation of analytical functions in Lp

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Exact asymptotic minimax constants for the estimation of analytical functions in L_p