GENERALIZED NEYMAN-PEARSON LEMMA VIA CONVEX DUALITY ⁄
GENERALIZED NEYMAN-PEARSON LEMMA VIA CONVEX DUALITY ⁄
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DOI：
10.2307/3318603
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发表时间：
2001-02
期刊：
影响因子：
1.5
通讯作者：
Jakša Cvitanić;I. Karatzas
中科院分区：
文献类型：
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作者：
Jakša Cvitanić;I. Karatzas
我们扩展了经典的奈曼-皮尔逊理论测试复合假设与复合替代品，使用凸对偶的方法，首先采用Witting。奥宾和Ekeland从非光滑凸分析的结果被使用，沿着Koml 6s定理，为了建立极大极小最优检验的存在性在相当大的一般性，并调查其性质。该理论说明了代表性的例子，涉及高斯措施欧几里德和维纳空间。
We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach, first employed by Witting. Results of Aubin and Ekeland from non-smooth convex analysis are used, along with a theorem of Koml6s, in order to establish the existence of a max-min optimal test in considerable generality, and to investigate its properties. The theory is illustrated on representative examples involving Gaussian measures on Euclidean and Wiener space.