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Asymptotic Improvement of the Usual Confidence Set in a Multivariate Normal Distribution with Unknown Variance


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  • Takada, Yoshikazu
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    We consider confidence sets for the mean of a multivariate normal distribution with unknown covariance matrix of the form[sigma]2I. The coverage probability of the usual confidence set is shown to be improved asymptotically by centering at a shrinkage estimator.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 64 (1998)
    Issue (Month): 2 (February)
    Pages: 118-130

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    Handle: RePEc:eee:jmvana:v:64:y:1998:i:2:p:118-130

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    Keywords: confidence set; coverage probability; asymptotic expansion; shrinkage estimator; and multivariate normal distribution;


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    1. Ullah, A. & Hwang, J.T., 1991. ""Confidence Sets Centered at James-Stein Estimators--A Surprise Concerning the Unknown Variance Case"," The A. Gary Anderson Graduate School of Management 92-36, The A. Gary Anderson Graduate School of Management. University of California Riverside.
    2. Robert, Christian & Casella, George, 1990. "Improved confidence sets for spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 84-94, January.
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