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Peter Dencker, Friedrich Liese

Local maximin properties of tests in Gaussian shift experiments

The local behavior of the power of weighted χ²-tests and Bayes tests is studied for simple null hypothesis in Gaussian shift experiments. A second order expansion of the power function is given. This expansion provides a shrinking family of ellipsoids (δE)_0<δ<1 so that the power of the weighted χ²-test is locally constant on the boundary ∂(δE). Approximating the weighted χ²-test by a sequence of Bayes tests with priors on ∂(δE), the weighted χ²-test is shown to be locally maximin in the sense of Giri and Kiefer [5] for the family of restricted alternatives given by the complements of the (δE)_0<δ<1.

Statistics & Decisions, Oldenbourg Wissenschaftsverlag

Print ISSN: 0721-2631
Volume: 22, 02/2004
Pages: 083 - 108

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