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Abstract Details
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Activity Number:
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424
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Type:
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Contributed
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Date/Time:
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Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #300872 |
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Title:
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Coherence in Hypotheses Testing
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Author(s):
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Rafael Izbicki*+ and Luís Gustavo Esteves
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Companies:
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Carnegie Mellon University and Universidade de Sao Paulo
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Address:
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3401 Forbes Avenue Apt 104, Pittsburgh, PA (PIT), PA, 15213, US
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Keywords:
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Simultaneous tests procedures ;
Decision Theory ;
Decision rules ;
Monotonicity
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Abstract:
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It is usual in Statistical Inference to simultaneously test a set of hypotheses concerning a parameter. Our aim is to evaluate the (lack of) logical coherence among conclusions obtained from tests conducted regarding the same data. In this study, we present a definition of class of hypotheses tests, a function that associates a test function to each hypothesis of interest. Some properties that reflect what one could expect (in terms of logical coherence) from tests for different hypotheses are then evaluated. These properties are exemplified by classes of hypotheses tests that satisfy them. Then, based on the properties studied, we propose sets of axioms regarding classes of hypotheses tests. Usual classes of hypotheses tests are investigated with satisfy to these sets of axioms. We analyze some properties related to these sets of axioms. At last, a result which connects hypotheses testing and point estimation is stated.
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