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Activity Number:
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459
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 1, 2007 : 2:00 PM to 4:50 PM
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Sponsor:
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IMS
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| Abstract - #309760 |
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Title:
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Double Shrinkage Empirical Bayesian Confidence Intervals for Multiple Parameters When the Variances Are Unequal and Unknown
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Author(s):
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Jing Qiu*+ and Gene J.T. Hwang and Zhigen Zhao
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Companies:
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University of Missouri-Columbia and Cornell University and Cornell University
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Address:
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134I Middlebush Hall, Columbia, MO, 65211,
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Keywords:
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Empirical Bayes ; Double shrinkage ; Multiple confidence intervals ; unequal and unknown variances ; microarray
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Abstract:
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In this paper we apply the empirical Bayes technique to construct confidence intervals for a large number $p$ of parameters. The present confidence intervals constructed in the literature assume that the variances $\sigma^2_i$'s are either known or equal. For the situation when variances are unequal and unknown, the suggestion is typically to replace it by an unbiased estimator $S^2_i$. However, when $p$ is large, there may be many $S^2_i$ that are extremely small and thus create many false positive results. This problem can be corrected by using shrinkage estimators. Here, we attempt to construct confidence intervals based on empirical Bayes estimators that shrink both the means and variances. Analytical and numerical studies and application to a real data show that compared to t intervals, our intervals have higher coverage probabilities while yielding shorter lengths.
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