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Some new statistics for testing hypotheses in parametric models

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Morales González, Domingo and Pardo Llorente, Leandro and Vadja, Igor (1997) Some new statistics for testing hypotheses in parametric models. Journal of multivariate analysis, 62 (1). pp. 137-168. ISSN 0047-259X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0047259X97916808


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Abstract

The paper deals with simple and composite hypotheses in statistical models with i.i.d. observations and with arbitrary families dominated by a finite measures and parametrized by vector-valued variables. It introduces phi-divergence testing statistics as alternatives to the classical ones: the generalized likelihood ratio and the statistics of Wald and Rao. It is shown that, under the assumptions of standard type about hypotheses and model densities, the results about asymptotic distribution of the classical statistics established so far for the counting and Lebesgue dominating measures (discrete and continuous models) remain true also in the general case. Further, these results are extended to the phi-divergence statistics with smooth convex functions phi. The choice of phi-divergence statistics optimal from the point of view of power is discussed and illustrated by several examples.


Item Type:Article
Uncontrolled Keywords:parametric models; simple and composite hypotheses; asymptotic distributions of rest statistics; generalized likelihood ratio; Wald's statistic; Rao's statistic; divergence statistics; divergence.
Subjects:Sciences > Mathematics > Applied statistics
ID Code:18118
Deposited On:01 Feb 2013 12:21
Last Modified:20 Jul 2018 08:46

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