Admissibility of the usual confidence set for the mean of a univariate or bivariate normal population: the unknown variance case

In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi. This solves a long-standing open problem in mathematical statistics, and this has important implications on t...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2017-06, Vol.79 (3), p.801-813
Main Authors: Leeb, Hannes, Kabaila, Paul
Format: Article
Language:English
Subjects:
Admissibility
Bivariate analysis
Confidence
Confidence intervals
Confidence set
Coverage probability
Economic models
Inference
Linear regression
Mathematical models
Regression analysis
Regression coefficients
Samples
Scale models
Shrinkage
Size
Statistical inference
Statistical methods
Statistics
Studies
Variance
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Summary:In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi. This solves a long-standing open problem in mathematical statistics, and this has important implications on the performance of modern inference procedures post model selection or post shrinkage, particularly in situations where the number of parameters is larger than the sample size. As a technical contribution of independent interest, we introduce a new class of conjugate priors for the Gaussian location-scale model.
ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12186