Robust slippage tests |
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Authors: | Miyoshi Kimura |
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Institution: | (1) Nanzan University, Nagoya, Japan |
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Abstract: | Summary The robust slippage testing problems ofk+1 approximately known simple hypotheses are formulated as the slippage testing problems ofk+1 composite hypotheses. It is shown that if there is a representativek+1-tuple (called a least favorable slippage tuple) of simple hypotheses, then maximin tests are given by the slippage analogues
of the Neyman-Pearson tests for this tuple. Thek-sample case is treated concerning this subject. In the general situations that there does not exist any least favorable slippage
tuple, a method for constructing tests is proposed and applied to the case that composite hypotheses are described in terms
of certain capacities (ε-contamination, total variation). The variants of the derived tests are also suggested. |
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