Optimal Confidence Sets, Bioequivalence, and the Limaçon of Pascal

We begin with a decision-theoretic investigation into confidence sets that minimize expected volume at a given parameter value. Such sets are constructed by inverting a family of uniformly most powerful tests, and hence they also enjoy the optimality property of being uniformly most accurate. In add...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1995-09, Vol.90 (431), p.880-889
Main Authors: Brown, Lawrence D., Casella, George, Gene Hwang, J. T.
Format: Article
Language:English
Subjects:
Bayes estimation
Bayesian analysis
Bioavailability
Bioequivalence
Biometrics
Confidence interval
Decision theory
Distribution theory
Equivalence relation
Exact sciences and technology
Frequentism
Frequentist estimation
Gaussian distributions
Hypotheses
Hypothesis
Hypothesis testing
Limacons
Mathematics
Normal distribution
Optimization
Probability
Probability and statistics
Property
Regression analysis
Sciences and techniques of general use
Statistical analysis
Statistical methods
Statistics
Theory and Methods
Therapeutic equivalency
Uniformly most accurate
Uniformly most powerful
Writing tablets
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Summary:We begin with a decision-theoretic investigation into confidence sets that minimize expected volume at a given parameter value. Such sets are constructed by inverting a family of uniformly most powerful tests, and hence they also enjoy the optimality property of being uniformly most accurate. In addition, these sets possess Bayesian optimal volume properties and represent the first case (to our knowledge) of a frequentist 1 - α confidence set that possesses a Bayesian optimality property. The hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing. Our sets are optimal for testing bioequivalence in certain settings; in the case of the normal distribution, the optimal set is a curve known as the limaçon of Pascal. We illustrate the use of these curves with a biopharmaceutical example.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1995.10476587