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A GEOMETRIC LOOK AT NUISANCE PARAMETER EFFECT

OF LOCAL POWERS IN TESTING HYPOTHESIS

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SHINTO EGUCHI

*Department of Mathematics, Shimane University, Matue 690, Japan*
(Received October 24, 1989; revised February 22, 1990)

**Abstract.**
This paper is concerned with the theory of
testing hypothesis with composite null hypothesis or with nuisance
parameters. The asymptotic behaviour of the likelihood ratio and the
associated test statistics are investigated. Under a class of local
alternatives with local orthogonality relative to the nuisance
parameter vector, a unique decomposition of local power is presented.
The decomposition consists of two parts; one is the influence of
nuisance parameters and the other is the power corresponding to the
simple case where the nuisance parameters are known. The
decomposition formula is applied to some examples, including the
gamma, Weibull and location-scale family.

*Key words and phrases*:
Curvature tensor, composite null
hypothesis, likelihood ratio, local power, local unbias, nuisance
parameters, variance coefficient.

**Source**
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