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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

## Abstract

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 |
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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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