Methods of Signal Processing

Second-Order Asymptotically Minimax Estimates for the Mean of a Normal Population

P. V. Berkhin, B. Ya. Levit


Abstract: The paper considers the classical problem of estimating a multidimensional parameter against a background of additive Gaussian noise. The first nontrivial term of the asymptotic expansion of the minimax risk of the estimate of a parameter belonging to bounded region $G\subset\mathbf R^k$ with piecewise-smooth boundary is investigated. Its relationship to the first eigenvalue of the Dirichlet problem in $G$ for some elliptic differential operator is established. The form of the second-order asymptotically minimax estimate is given.

UDC: 621.391.1:519.27

Received: 03.04.1979

 English version: Problems of Information Transmission, 1980, 16:3, 212–229

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