Minimax detection of a signal for nondegenerate loss functions, and extremal convex problems
Minimax detection of a signal for nondegenerate loss functions, and extremal convex problems
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非简并损失函数信号的极小极大检测和极值凸问题
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发表时间：
1999
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通讯作者：
Yu. I. Ingster
中科院分区：
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作者：
Yu. I. Ingster
研究了一类广泛的非参数选择下信号检测的极大极小问题，以及一类特殊损失函数对这些问题的修正。在相当一般的假设下，我们得到了极大极小误差概率的精确渐近性（高斯型）和极大极小检验的结构。该方法将所考虑的问题简化为实线上概率测度序列凸集上某希尔伯特范数的极小化极值问题。在I. a . Suslina的一篇论文中，研究了带有lq-椭球的lq-椭球类型的替代方案的这些极值问题。参考书目：16篇。
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.