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Construction of minimax-tests for bounded families of probability-densities

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Summary

A new method for the construction of least favourable pairs of densities and of minimaxtests is given for the compound test-problem\(H_0 :\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{g} \leqslant f \leqslant \bar g\) against\(H_1 :\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{f} \leqslant f \leqslant \bar f\), the bounds\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{g} ,\bar g,f,\bar f\) being fixed. The main tool of the method is the risk-function for simple test-problems.

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  1. Institut für Angewandte Statistik, Johannes-Kepler- Universität Linz, 4045, Linz/Auhof, Austria

    Robert Hafner

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  1. Robert Hafner
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Hafner, R. Construction of minimax-tests for bounded families of probability-densities. Metrika 40, 1–23 (1993). https://doi.org/10.1007/BF02613659

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  • DOI: https://doi.org/10.1007/BF02613659

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