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Monotonicity of the power function and unbiasedness of some likelihood ratio tests

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Abstract

A natural generalization of thep-dimensional normal distribution is provided by elliptically contoured distributions. In the case of the normal distribution the likelihood ratio tests (LRT) of null-hypothesis of the form

$$\Sigma = I,$$
(i))
$$\Sigma = I and \mu = 0,$$
(ii))

have well known properties. This paper contains an investigation of the question of how far these properties are conserved when this more general family of distributions is considered. It is shown that the unbiasedness of the tests and the monotonicity of rheir power functions can still be proved for a large subfamily of these distributions.

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Chen, L. Monotonicity of the power function and unbiasedness of some likelihood ratio tests. Metrika 36, 149–159 (1989). https://doi.org/10.1007/BF02614087

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  • DOI: https://doi.org/10.1007/BF02614087

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