Geodesic
Asymptotically optimal Bayesian tests for composite hypotheses
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 738-757 
Yu. I. Ingster. Asymptotically optimal Bayesian tests for composite hypotheses. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 738-757. http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a10/
@article{TVP_1983_28_4_a10,
     author = {Yu. I. Ingster},
     title = {Asymptotically optimal {Bayesian} tests for composite hypotheses},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {738--757},
     year = {1983},
     volume = {28},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider two asymptotical ($\varepsilon\to 0$) problems of testing hypotheses $H_{0,\varepsilon}=\{P_{\varepsilon,\theta},\,\theta\in\Theta_0\}$ against $H_\varepsilon=\{P_{\varepsilon,\theta},\,\theta\in\Theta\diagdown\Theta_0\}$ with $\Theta_0\subset E^m$ being the subset of the parameter space $\Theta\subset E^n$, $0\le m. Under sufficiently general assumptions about the families $P_{\varepsilon,\theta}$ and the densities $\pi_\varepsilon$ and $\pi_{\varepsilon,0}$ on $\Theta\diagdown\Theta_0$ and $\Theta_0$ we construct asymptotically optimal famalies of Bayesian tests and investigate the asymptotics of probabilities of errors.