Universidad Complutense de Madrid
E-Prints Complutense

Rényi statistics for testing composite hypotheses in general exponential models.

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Morales González, Domingo y Pardo Llorente, Leandro y Pardo Llorente, María del Carmen y Vadja, Igor (2004) Rényi statistics for testing composite hypotheses in general exponential models. Statistics, 38 (2). pp. 133-147. ISSN 0233-1888

URL Oficial: http://www.tandfonline.com/doi/abs/10.1080/02331880310001634647


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http://www.tandfonline.com/Editorial


Resumen

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.


Tipo de documento:Artículo
Palabras clave:natural exponential models; testing composite hypotheses; generalized likelihood ratio statistics; generalized Wald statistics; Renyi statistics; hypotheses about Levy processes; families.
Materias:Ciencias > Matemáticas > Estadística matemática
Código ID:17740
Depositado:17 Ene 2013 09:09
Última Modificación:17 Ene 2013 09:09

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