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Extremum problems in minimax signal detection for \(L_q\)-ellipsoids with an \(l_p\)-ball removed. (English. Russian original) Zbl 0935.62055
J. Math. Sci., New York 93, No. 3, 454-469 (1999); translation from Zap. Nauchn. Semin. POMI 228, 312-332 (1996).
Summary: An asymptotic minimax problem of signal detection for signals from \(l_q\)-ellipsoids with an \(l_p\)-ball removed \((p>2\) or \(q<p<2)\) in a Gaussian white noise is considered. Asymptotically sharp distinguishability conditions and some estimates of the minimax probability of errors of signal detection for ellipsoids with axes \(a_n\asymp n^{-\lambda}\), \(\lambda>0\), are obtained. The proofs use results and techniques developed by Yu.I. Ingster [see the preceding review, Zbl 0935.62054].
MSC:
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
62C20 Minimax procedures in statistical decision theory
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References:
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[2] M. S. Ermakov, ”Minimax detection of a signal in a Gaussian white noise,”Teor. Veroyatn. Primen.,35, 667–679 (1990). · Zbl 0744.62117
[3] Yu. I. Ingster, ”Minimax detection of signals inl p -metrics,”Zap. Nauchn. Semin. LOMI,184, 152–168 (1990). · Zbl 0738.94005
[4] I. A. Suslina, ”Minimax detection of a signal forl q -ellipsoids with anl p -ball removed,”Zap. Nauchn. Semin. POMI,207, 127–137 (1993).
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[6] Yu. I. Ingster, ”Minimax detection of a signal for nondegenerate loss functions and convex extremal problems,”Zap. Nauchn. Semin. POMI,228, 162–188 (1996). · Zbl 0935.62054
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