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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
##### Citations:
Zbl 0880.00018; Zbl 0913.00023; Zbl 0935.62054; Zbl 0935.62085
Full Text:
##### References:
 [1] Yu. I. Ingster, ”On the minimax nonparametric detection of signals in a Gaussian white noise,”Probl. Pered. Inf.,18, No. 2, 130–140 (1982). · Zbl 0499.94002 [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). [5] Yu. I. Ingster, ”Asymptotically minimax hypothesis testing for nonparametric alternatives. I–III,”Math. Methods Stat.,2, 85–114, 171–189, 249–268 (1993). · Zbl 0798.62057 [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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