Empirical Bayes confidence intervals shrinking both means and variances

We construct empirical Bayes intervals for a large number p of means. The existing intervals in the literature assume that variances [graphic removed] are either equal or unequal but known. When the variances are unequal and unknown, the suggestion is typically to replace them by unbiased estimators...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2009-01, Vol.71 (1), p.265-285
Main Authors: Gene Hwang, J.T, Qiu, Jing, Zhao, Zhigen
Format: Article
Language:English
Subjects:
Bayes estimators
Bayesian analysis
Bayesian method
Bias
Confidence interval
Confidence intervals
Data analysis
Decision theory
Degrees of freedom
Empirical research
Estimation
Estimators
Exact sciences and technology
General topics
Mathematical intervals
Mathematics
Modeling
Multiple testing
Musical intervals
Nonparametric inference
Parametric inference
Probability and statistics
Quantitative analysis
Random variables
Research methods
Sciences and techniques of general use
Shrinkage
Shrinking both means and variances
Shrinking means
Shrinking variances
Simulation
Simultaneous confidence intervals
Statistical discrepancies
Statistical methods
Statistics
Studies
Variance
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Summary:We construct empirical Bayes intervals for a large number p of means. The existing intervals in the literature assume that variances [graphic removed] are either equal or unequal but known. When the variances are unequal and unknown, the suggestion is typically to replace them by unbiased estimators [graphic removed] . However, when p is large, there would be advantage in 'borrowing strength' from each other. We derive double-shrinkage intervals for means on the basis of our empirical Bayes estimators that shrink both the means and the variances. Analytical and simulation studies and application to a real data set show that, compared with the t-intervals, our intervals have higher coverage probabilities while yielding shorter lengths on average. The double-shrinkage intervals are on average shorter than the intervals from shrinking the means alone and are always no longer than the intervals from shrinking the variances alone. Also, the intervals are explicitly defined and can be computed immediately.
ISSN:1369-7412
1467-9868
DOI:10.1111/j.1467-9868.2008.00681.x