TESTS WITH CONDITIONAL FREQUENTISTS ERRORS AND TESTS WITH INTERPRETATION BAYESIAN AND CONDITIONAL FREQUENTISTS. / TESTES COM ERROS FREQÃENTISTAS CONDICIONAIS E TESTES COM INTERPRETAÃÃO BAYESIANA E FREQÃENTISTA CONDICIONAL

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

The Neyman-Pearson tests of hypotheses present probabilities of error independent of the observed data; this is an enormous source of critics. In the significance tests the p-value is used, but this is not a frequentist measuring.Kiefer (1977) formalized a frequentist methodology dependent of the data. The sample space is partitioned using a partitioning function and it is developed measure a conditional frequentist error, denominated conditional error probabilities (CEP). The critical value and CEPâs of a test depend on the used partition. Berger, Brown and Wolpert (1994) observed that in the Bayesian test between two simple hypotheses, for certain types of losses function and priors densities, it would be a genuine conditional frequentist test too. But, there are some cases that some problematic situations can happen, so they proposed the incorporation of a âno-decision regionâ, NDR, whose objective is to avoid the presence of the CEPâs (or posterior probabilities) greater to 0,5. The objective of this work in chapter 1 was to review the details of the tests of hypothesis and test of significance, emphasizing the main differences and critics. In chapter 2, the objective was the development in details of all the mathematic theory of the tests with conditioning frequentists errors using one function H(x), denominated âpartitioning functionâ and to analyze the CEPâs when it is used four criteria of partition based on the âancillaryâ statistic, in the âintrinsic significance levelâ, in the âequal probability continuumâ and in âp-valuesâ and also to examine the relation of them with the symmetry of the likelihood ratio. In chapter 3, the objectives were the exam of the effect of the NDR incorporation in the unified test in some examples and study its behavior in cases of asymmetrical losses. In the case of symmetry of the likelihood ratio, all the used conditioning statistics agreed. In the case when the likelihood ratio is asymmetrical, some divergences appeared. The conditioning with the equal conditional errors and based on pvalues was the best. Regarding the size of the NDR, the conclusion was that the developed examples are dependent of the size of the sample, and that some kind of losses l, can make the test inadequate.

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agronomia

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