In the framework of standard model of asymptotic statistics we introduce a global information in the statistical experiment about the occurrence of the true parameter in a given set. Basic properties of this information are established, including relations to the Kullback and Fisher information. Its applicability in point estimation and testing statistical hypotheses is demonstrated.
The concept of global statistical information in the classical statistical experiment with independent exponentially distributed samples is investigated. Explicit formulas are evaluated for common exponential families. It is shown that the generalized likelihood ratio test procedure of model selection can be replaced by a generalized information procedure. Simulations in a classical regression model are used to compare this procedure with that based on the Akaike criterion.
The aim of the paper is to present a test of goodness of fit with weigths in the classes based on weighted -divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [frank] and Kapur [kapur]. The weighted -divergence between an empirical distribution and a fixed distribution is here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear...
In this paper a new family of statistics based on -divergence for testing goodness-of-fit under composite null hypotheses are considered. The asymptotic distribution of this test is obtained when the unspecified parameters are estimated by maximum likelihood as well as minimum -divergence.
We construct a new class of data driven tests for uniformity, which have greater average power than existing ones for finite samples. Using a simulation study, we show that these tests as well as some "optimal maximum test" attain an average power close to the optimal Bayes test. Finally, we prove that, in the middle range of the power function, the loss in average power of the "optimal maximum test" with respect to the Neyman-Pearson tests, constructed separately for each alternative, in the Gaussian...
En el contexto de información e incertidumbre generalizada, establecido por J. Kampé de Fériet y B. Forte, se axiomatizan las medidas de incertidumbre e información condicionada y se determinan tales medidas bajo la hipótesis de total componibilidad de las mismas.
En el presente artículo se utiliza el método de maximización de la información desconocida para deducir las distribuciones inicial y final de referencia cuando se trata de hacer inferencias sobre el coeficiente de correlación de una población normal bivariante.
A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected...
The Fisher information matrices are derived for three of the most popular elliptically symmetric distributions: the Pearson type II, Pearson type VII and the Kotz type distributions. We hope the results could be important to the many researchers working in this area.
The exact range of the joined values of several Rényi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied. Like in the case when only two orders of the Rényi entropies are studied, one can parametrize the boundary of the range. An explicit formula for a tight upper or lower bound for one order of entropy in terms of another order of entropy cannot be given.
En este trabajo se establece un criterio de comparación entre sistemas de información difusa basado en la maximización de la energía informacional esperada de orden α y tipo β y se comprueba que verifica las propiedades más relevantes que a nuestro juicio debe verificar un criterio de comparación.
En esta comunicación se establece una medida de la entropía contenida en un proceso puntual mediante el concepto de entropía de orden α y tipo β introducida por Sharma and Mittal (1975); quedando, de este modo, generalizada la entropía de McFadden. Una vez que se estudian las propiedades relativas a la tasa de cambio de la Entropía, se demuestra que el proceso de Poisson es el de Entropía máxima dentro de la clase de los procesos puntuales estacionarios.