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The Optimal Confidence Region for a Random Parameter

Author

Listed:
  • Hajime Uno

    (Harvard University)

  • Lu Tian

    (Northwestern University)

  • L.J. Wei

    (Harvard University)

Abstract

Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide gene-expession data for estimating individual gene- or center-specific parameters simultaneously. The new proposal is illustrated with a typical microarray data set and its performance is examined via a small simulation study.

Suggested Citation

  • Hajime Uno & Lu Tian & L.J. Wei, 2004. "The Optimal Confidence Region for a Random Parameter," Harvard University Biostatistics Working Paper Series 1013, Berkeley Electronic Press.
    • Handle: RePEc:bep:hvdbio:1013
    Note: oai:bepress.com:harvardbiostat-1013
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    References listed on IDEAS

    as
    1. Gauri Sankar Datta & Malay Ghosh & David Daniel Smith & Parthasarathi Lahiri, 2002. "On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 139-152, March.
    Full references (including those not matched with items on IDEAS)

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