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Activity Number:
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543
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Type:
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Contributed
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Date/Time:
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Thursday, August 10, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Biometrics Section
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| Abstract - #305573 |
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Title:
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Preliminary Test Estimator for the Mean of Bivariate Normal
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Author(s):
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Xiaoping Zhu*+ and Chien-Pai Han
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Companies:
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Novartis Pharmaceuticals Corporation and The University of Texas at Arlington
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Address:
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180 Park Ave., Florham Park, NJ, 09832,
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Keywords:
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preliminary test estimator ; bivariate normal distribution ; bias ; risk ; relative efficiency
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Abstract:
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This paper considers the estimation of the population mean of a bivariate normal distribution with unknown covariance matrix when prior information about the mean is available. The prior information is that the mean vector is equal to a given value, but this information is uncertain. The experimenter should then test the validity of the prior information by bivariate test or univariate tests (i.e. testing each component mean individually). Hence, preliminary test estimator (PTE) can be constructed to estimate the population mean. The biases and relative efficiencies of the PTE using the bivariate test and the PTE using the univariate test are discussed. The behavior of the bias for both tests is studied. The risk of the PTE is analyzed using relative efficiency with respect to the usual estimator. It is shown that, for certain sample sizes and significance levels, the PTE performs better.
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