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May, 1982 Minimax Linear Smoothing for Capacities
H. Vincent Poor
Ann. Probab. 10(2): 504-507 (May, 1982). DOI: 10.1214/aop/1176993874


Minimax linear smoothers are considered for the problem of estimating a homogeneous signal field in an additive orthogonal noise field. A minimax game with the quadratic-mean estimation error as an objective function is used to formulate this problem. Uncertainty in signal and noise field spectra is modeled using general nonparametric classes of measures proposed by Huber and Strassen for the problem of minimax hypothesis testing. These classes, which are described in terms of Choquet alternating capacities of order 2, include the conventional models for spectral uncertainty and admit a general solution to the minimax linear smoothing problem.


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H. Vincent Poor. "Minimax Linear Smoothing for Capacities." Ann. Probab. 10 (2) 504 - 507, May, 1982.


Published: May, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0504.62085
MathSciNet: MR665605
Digital Object Identifier: 10.1214/aop/1176993874

Primary: 62M20
Secondary: 60G35 , 93E11

Keywords: Choquet capacities , Minimax smoothing , Random fields

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • May, 1982
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