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Título:
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Rényi statistics for testing composite hypotheses in general exponential models.
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Autores:
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Morales González, Domingo ;
Pardo Llorente, Leandro ;
Pardo Llorente, María del Carmen ;
Vadja, Igor
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Tipo de documento:
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texto impreso
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Editorial:
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Taylor & Francis, 2004-04
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Estadística matemática
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Tipo = Artículo
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Resumen:
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We introduce a family of Renyi statistics of orders r is an element of R for testing composite hypotheses in general exponential models, as alternatives to the previously considered generalized likelihood ratio (GLR) statistic and generalized Wald statistic. If appropriately normalized exponential models converge in a specific sense when the sample size (observation window) tends to infinity, and if the hypothesis is regular, then these statistics are shown to be chi(2)-distributed under the hypothesis. The corresponding Renyi tests are shown to be consistent. The exact sizes and powers of asymptotically alpha-size Renyi, GLR and generalized Wald tests are evaluated for a concrete hypothesis about a bivariate Levy process and moderate observation windows. In this concrete situation the exact sizes of the Renyi test of the order r = 2 practically coincide with those of the GLR and generalized Wald tests but the exact powers of the Renyi test are on average somewhat better.
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