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Activity Number:
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26
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Type:
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Contributed
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Date/Time:
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Sunday, July 29, 2007 : 2:00 PM to 3:50 PM
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Sponsor:
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General Methodology
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| Abstract - #309404 |
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Title:
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The Equivalence Between Selecting and Hypothesis Testing
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Author(s):
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Weixing Cai*+ and Pinyuen Chen
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Companies:
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Syracuse University and Syracuse University
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Address:
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Department of Mathematics, Syracuse, NY, 13210,
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Keywords:
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Correct selection ; hypothesis testing ; stepwise procedure ; least favorable configuration, ; Mahalanobis distance ; operating characteristic functions
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Abstract:
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We consider various definitions of positive and negative populations, and define the corresponding "correct selection" (CS) for different selection goals. Depending on whether the covariance matrices are known or unknown, we propose single-step and stepwise procedures to achieve the goals of selecting populations that are equivalent to a given standard or a control by using Mahalanobis distance function for multivariate case(p>1). The univariate case will be considered as a special case where a standardized location distance is considered. The equivalence between selecting and hypothesis testing, including multiple hypothesis testing, is also established. Least favorable configurations are proved. Tables and graphs are presented to illustrate the properties of operating characteristic functions. Simulation examples will be given. Other forms of hypothesis testing will also be mentioned.
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