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Directional monotonicity properties of the power functions of likelihood ratio tests for cone-restricted hypotheses of normal means

โœ Scribed by Manabu Iwasa

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
505 KB
Volume
66
Category
Article
ISSN
0378-3758

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โœฆ Synopsis

In some cone-restricted testing problems, it is known that the power function of the likelihood ratio test has a certain monotonicity property with respect to the direction of the alternatives. In this paper, we establish a unified result concerning such directional monotonicity by using an argument based on a cone ordering and a related probability inequality. From this result, we show that the power function is unimodal in direction when the cone is suitably symmetric.

๐Ÿ“œ SIMILAR VOLUMES

On the Power Function of the Likelihood
On the Power Function of the Likelihood Ratio Test for MANOVA
โœ Dulal Kumar Bhaumik; Sanat K. Sarka ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 77 KB

We prove that the power function of the likelihood ratio test for MANOVA attains its minimum when the rank of the location parameter matrix G decreases from s to 1. This provides a theoretical justification of a result that is known in the literature based only on numerical studies.