<title>Anomalous signal detection and estimation on the stochastic noise background</title>
Shakir Kasimovich FormanovInstitute of Mathematics (Uzbekistan)Anatoliy N. StartsevInstitute of Mathematics (Uzbekistan)Olimshan Sh. SharipovInstitute of Mathematics (Uzbekistan)Jakhongir B. AzimovInstitute of Mathematics (Uzbekistan)
Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEjournal2006en
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The problem of the minimax recovery of a nonparametric two-dimensional signal blurred by some khown function and observed with additive noise is considered. The unknown function of two variables is assumed to belong to a hyperrectangle of L<sub>2</sub>([0,1]<sup>2</sup>) Under some conditions, we find the exact asymptotic behavior of the quadratic minimax risk. We propose linear minimax estimator and show that its maximal risk attains asymptotically the minimax risk. In the case of non-Gaussian noise we propose other estimator that however is not asymptotically optimal.
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