A note on testing two-dimensional normal mean
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For the problem of testing a composite hypothesis with one-sided alternatives of the mean vector of a two-dimensional normal distribution, a characterization of similar tests is presented and an unbiased test dominating the likelihood ratio test is proposed. A sufficient condition for admissibility is given, which implies the result given by Cohen et al. (1983,Studies in Econometrics, Time Series and Multivariate Statistics, Academic Press): the admissibility of the likelihood ratio test.
Key words and phrasesComposite hypothesis one-sided alternatives Schur-concave function unbiased test admissibility
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- Cohen, A., Gatsonis, C. and Marden, J. I. (1983b). Hypothesis tests and optimality properties in discrete multivariate analysis, inStudies in Econometrics, Time Series and Multivariate Statistics, Academic Press.Google Scholar