A note on the power superiority of the restricted likelihood ratio test

Jens Praestgaard

Journal of Multivariate Analysis, 2012, vol. 104, issue 1, 1-15

Abstract: Let be a closed convex cone which contains a linear subspace . We investigate the restricted likelihood ratio test for the null and alternative hypotheses based on an n-dimensional, normally distributed random vector (X1,...,Xn) with unknown mean and known covariance matrix [Sigma]. We prove that if the true mean vector satisfies the alternative hypothesis HA, then the restricted likelihood ratio test is more powerful than the unrestricted test with larger alternative hypothesis [real]n. The proof uses isoperimetric inequalities for the uniform distribution on the n-dimensional sphere and for n-dimensional standard Gaussian measure.

Keywords: Order; restricted; inference; Convex; cone; Gaussian; isoperimetric; inequality (search for similar items in EconPapers)
Date: 2012
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