Abstract
Let (P ϑ : ϑ εR p) be a simple shift family of distributions onR p, and letK ⊂R p be a convex cone. Within the class of nonrandomized tests ofK versusR p∖K, whose acceptance regionA satisfiesA=A+K, a test with minimal bias is constructed. This minimax test is compared to a likelihood ratio type test, which is optimal with respect to a different criterion. The minimax test is mimicked in the context of linear regression and one-sided tests for covariance matrices.
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References
Akkerboom, J. C. (1990). Testing problems with linear or angular inequality constraints,Lecture Notes in Statist.,62, Springer, Berlin.
Dunnett, C. W. (1955). A multiple comparisons procedure for comparing several treatments with a control,J. Amer. Statist. Assoc.,50, 1096–1121.
Kuriki, S. (1993). Likelihood ratio tests for covariance structure in random effects models,J. Multivariate Anal.,46, 175–197.
Lehmann, E. L. (1986).Testing Statistical Hypotheses, 2nd ed., Wiley, New York.
Robertson, T., Wright, F. T. and Dykstra, R. L. (1988).Order Restricted Statistical Inference, Wiley, New York.
Rockafellar, R. T. (1970).Convex Analysis, Princeton University Press, New Jersey.
Roy, S. N. (1957).Some Aspects of Multivariate Analysis, Wiley, New York.
Stein, C. (1956). The admissibility of Hotelling'sT 2-test,Ann. Math. Statist.,27, 616–623.
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Dümbgen, L. Minimax tests for convex cones. Ann Inst Stat Math 47, 155–165 (1995). https://doi.org/10.1007/BF00773419
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DOI: https://doi.org/10.1007/BF00773419