Improved Confidence Statements for the Usual Multivariate Normal Confidence Set

  • Christian Robert
  • George Casella


The usual multivariate normal confidence set has reported confidence 1—α, which is equal to its coverage probability. If we take a decision theoretic view, and attempt to estimate the coverage, we find that 1— α is an inadmissible estimator in more than four dimensions. We establish this fact and, moreover, exhibit adaptive confidence estimators that appear to dominate 1— α. These new confidence estimators are developed through empirical Bayes arguments and approximations. They allow us to attach confidence that is uniformly greater than 1— α. We provide necessary conditions, and strong numerical evidence to support our domination claims.


Confidence Statement Coverage Probability Confidence Estimator Error Loss Confidence Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Christian Robert
    • 1
  • George Casella
    • 2
  1. 1.Université Paris VIFrance
  2. 2.Cornell UniversityUSA

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