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On testing against restricted alternatives about the means of Gaussian models with common unknown variance. (English) Zbl 0687.62020

Summary: Let \(\pi_ 1,\pi_ 2,...,\pi_ k\) be k independent Gaussian populations with unknown means \(\mu_ 1,\mu_ 2,...,\mu_ k\), respectively, and common but unknown variance \(\sigma^ 3\). A k-sample extension of the two-sample one-sided t-test is developed for testing \(H_ 0:\) \(\mu_ 1=\mu_ 2=...=\mu_ k\) against \(H_ 1:\) \(\mu_ 1\leq \mu_ 2\leq...\leq \mu_ k\) with at least one strict inequality. Some optimality properties of the test are also discussed.

MSC:

62F03 Parametric hypothesis testing
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