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| Author(s): |
Rafael Izbicki
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2010-06-08 |
| Examining board members: |
Luís Gustavo Esteves;
Veronica Andrea Gonzalez Lopez;
Sergio Wechsler
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| Advisor: | Luís Gustavo Esteves |
| Abstract | |
In Statistical Inference, it is usual, after an experiment is performed, to test simultaneously a set of hypotheses of interest concerning an unknown parameter. Therefore, to each hypothesis, a statistical test is performed and a conclusion about the parameter is drawn based on it. The objective of this work is to evaluate the (lack of) logical coherence among conclusions obtained from tests conducted after the observation of a single experiment. In this study, a definition of class of hypotheses tests, a function that associates a test function to each hypothesis of interest, is presented. Some properties that reflect what one could expect (in terms of logical coherence) from tests to different hypotheses are then evaluated. These properties are exemplified by classes of hypotheses tests that respect them. Then, sets of axioms based on the properties studied are proposed to classes of hypotheses tests. Usual classes of hypotheses tests are investigated with respect to these sets of axioms. Some properties related to these sets of axioms are then analyzed. At last, a result which seems to connect hypotheses testing and point estimation is stated. (AU) | |
| FAPESP's process: | 09/03385-5 - Classes of hypotheses tests |
| Grantee: | Rafael Izbicki |
| Support Opportunities: | Scholarships in Brazil - Master |