Advertisement

Minimax tests for convex cones

  • Lutz Dümbgen
Tests

Abstract

Let (Pϑ : ϑ εR p ) be a simple shift family of distributions onR p , and letKR 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.

Key words and phrases

Bias convex cone covariance matrix duality linear regression minimax test union-intersection principle 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akkerboom, J. C. (1990). Testing problems with linear or angular inequality constraints,Lecture Notes in Statist.,62, Springer, Berlin.Google Scholar
  2. Dunnett, C. W. (1955). A multiple comparisons procedure for comparing several treatments with a control,J. Amer. Statist. Assoc.,50, 1096–1121.Google Scholar
  3. Kuriki, S. (1993). Likelihood ratio tests for covariance structure in random effects models,J. Multivariate Anal.,46, 175–197.Google Scholar
  4. Lehmann, E. L. (1986).Testing Statistical Hypotheses, 2nd ed., Wiley, New York.Google Scholar
  5. Robertson, T., Wright, F. T. and Dykstra, R. L. (1988).Order Restricted Statistical Inference, Wiley, New York.Google Scholar
  6. Rockafellar, R. T. (1970).Convex Analysis, Princeton University Press, New Jersey.Google Scholar
  7. Roy, S. N. (1957).Some Aspects of Multivariate Analysis, Wiley, New York.Google Scholar
  8. Stein, C. (1956). The admissibility of Hotelling'sT 2-test,Ann. Math. Statist.,27, 616–623.Google Scholar

Copyright information

© The Institute of Statistical Mathematics 1995

Authors and Affiliations

  • Lutz Dümbgen
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergGermany

Personalised recommendations