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Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 4, Pages 738–757 (Mi tvp2221)  

Asymptotically optimal Bayesian tests for composite hypotheses

Yu. I. Ingster

Leningrad

Abstract: 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 $\Theta\subset E^n$, $0\le m<n$. 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.

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English version:
Theory of Probability and its Applications, 1984, 28:4, 775–794

Bibliographic databases:

Received: 23.05.1981

Citation: Yu. I. Ingster, “Asymptotically optimal Bayesian tests for composite hypotheses”, Teor. Veroyatnost. i Primenen., 28:4 (1983), 738–757; Theory Probab. Appl., 28:4 (1984), 775–794

Citation in format AMSBIB
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\paper Asymptotically optimal Bayesian tests for composite hypotheses
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 4
\pages 738--757
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\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 4
\pages 775--794
\crossref{https://doi.org/10.1137/1128075}
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