This paper deals with Bayesian models given by statistical experiments and standard loss functions. Bayes probability of error and Bayes risk are estimated by means of classical and generalized information criteria applicable to the experiment. The accuracy of the estimation is studied. Among the information criteria studied in the paper is the class of posterior power entropies which include the Shannon entropy as special case for the power $\alpha =1$. It is shown that the most accurate estimate is in this...

Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the value function is described by a conic core, a modification of the earlier concept of convex core. Minimizers...

La Geometría estadística es un método complementario a los desarrollados hasta el momento para la inferencia y evaluación de las relaciones filogenéticas entre entidades emparentadas, y que permite decidir si la estructura filogenética obtenida tiene una configuración de árbol, de estrella o de red.El objetivo de este trabajo consiste en poner de manifiesto que, si bien la geometría estadística puede ayudar a decidir entre grandes topologías, no puede decidir entre tipos específicos de topologías....

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 $\left(h,\phi \right)$-divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [frank] and Kapur [kapur]. The weighted $\left(h,\phi \right)$-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 $K_{\phi }$-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 $K_{\phi }$-divergence.