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Minimax detection of a signal for nondegenerate loss functions, and extremal convex problems

Research paper by Yu. I. Ingster

Indexed on: 01 Feb '99Published on: 01 Feb '99Published in: Journal of Mathematical Sciences



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.