Minimax detection of a signal for nondegenerate loss functions, and extremal convex problems |
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Authors: | Yu I Ingster |
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Abstract: | We study a wide class of minimax problems of signal detection under nonparametric alternatives and a modification of these
problems for a special class of loss functions. Under rather general assumptions, we obtain the exact asymptotics (of Gaussian
type) for the minimax error probabilities and the structure of asymptotically minimax tests. The methods are based on a reduction
of the problems under consideration to extremal problems of minimization of a certain Hilbert norm on a convex set of sequences
of probability measures on the real line. These extremal problems are investigated in a paper by I. A. Suslina for alternatives
having the type of lq-ellipsoids with lp-balls removed. Bibliography: 16 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 162–188. |
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