Probability Theory
The Neyman–Pearson lemma under g-probability
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 209-212.

The Neyman–Pearson fundamental lemma is generalized under g-probability. With convexity assumptions, a sufficient and necessary condition which characterizes the optimal randomized tests is obtained via a maximum principle for stochastic control.

Le lemme fondamental de Neyman–Pearson est généralisé au cas de g-probabilités. Sous des hypothèses de convexité, une condition suffisante et nécessaire caractérisant le test randomisé optimal est obtenue au moyen du principe du maximum dans le cadre du contrôle stochastique.

Published online:
DOI: 10.1016/j.crma.2007.12.007
Ji, Shaolin 1; Zhou, Xun Yu 2, 3

1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China
2 Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
3 Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong
     author = {Ji, Shaolin and Zhou, Xun Yu},
     title = {The {Neyman{\textendash}Pearson} lemma under \protect\emph{g}-probability},
     journal = {Comptes Rendus. Math\'ematique},
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Ji, Shaolin; Zhou, Xun Yu. The Neyman–Pearson lemma under g-probability. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 209-212. doi : 10.1016/j.crma.2007.12.007.

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Cited by Sources:

The authors thank the partial support from the National Basic Research Program of China (973 Program, No. 2007CB814900), the RGC Earmark Grant No. 418606, and a start-up fund at Oxford.

⁎⁎ This Note is the succinct version of a text on file for five years in the Academy Archives.