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Rényi statistics for testing composite hypotheses in general exponential models.



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

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


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.

Item Type:Article
Uncontrolled Keywords:natural exponential models; testing composite hypotheses; generalized likelihood ratio statistics; generalized Wald statistics; Renyi statistics; hypotheses about Levy processes; families.
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:17740
Deposited On:17 Jan 2013 09:09
Last Modified:17 Jan 2013 09:09

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