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Existence, Consistency and computer simulation for selected variants of minimum distance estimators

Václav Kůs, Domingo Morales, Jitka Hrabáková, Iva Frýdlová (2018)

Kybernetika

The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function f 0 on the real line. It shows that the AMDE always exists when the bounded φ -divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, n - 1 / 2 consistency rate in any bounded φ -divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding family...

Extensión del concepto de energía informacional de Onicescu basado en el análisis no estandar.

Leandro Pardo (1985)

Trabajos de Estadística e Investigación Operativa

En esta comunicación, a partir del concepto de energía informacional de Onicescu para variables aleatorias discretas, se da el concepto de energía informacional para cualquier tipo de variables aleatorias como una extensión del anterior basándonos en el análisis no estándar de Robinson (1960). Se estudian sus propiedades y se analiza, en particular, su comportamiento con respecto a la energía informacional de Onicescu en caso de variables aleatorias continuas.

Extensions of the Frisch-Waugh-Lovell Theorem

Jürgen Groß, Simo Puntanen (2005)

Discussiones Mathematicae Probability and Statistics

In this paper we introduce extensions of the so-called Frisch-Waugh-Lovell Theorem. This is done by employing the close relationship between the concept of linear sufficiency and the appropriate reduction of linear models. Some specific reduced models which demonstrate alternatives to the Frisch-Waugh-Lovell procedure are discussed.

Factorized mutual information maximization

Thomas Merkh, Guido F. Montúfar (2020)

Kybernetika

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual information of two subsets of variables, at a lower computation and estimation complexity. We describe the maximizers and their relations to the maximizers of the multi-information and the mutual information.

Filtering of signals transmitted in multichannel from Chandrasekhar and Riccati recursions.

S. Nakamori, A. Hermoso, J. Jiménez, J. Linares (2005)

Extracta Mathematicae

In this paper two recursive algorithms are proposed and compared as a solution of the least mean-squared error linear filtering problem of a wide-sense stationary scalar signal from uncertain observations perturbed by white and coloured additive noises. Considering that the state-space model of the signal is not available and that the variables modelling the uncertainty are not independent, the proposed algorithms are derived by using covariance information. The difference between both algorithms...

Funcionales de mínima g-divergencia y sus estimadores asociados (II).

Francisco Javier Cano Sevilla, M.ª Pilar Lasala Calleja (1984)

Trabajos de Estadística e Investigación Operativa

Se realizan dos estudios de simulación para comprobar el comportamiento asintóticamente robusto del estimador de mínima g-divergencia para dos elecciones notables de la función g.

Funcionales de mínima g-divergencia y sus estimadores asociados (I).

Francisco José Cano Sevilla, M.ª Pilar Lasala Calleja (1984)

Trabajos de Estadística e Investigación Operativa

Se introducen los funcionales de mínima g-divergencia y sus estimadores asociados. Se prueba la existencia y robustez del funcional y la convergencia del estimador asociado.

Further results on the generalized cumulative entropy

Antonio Di Crescenzo, Abdolsaeed Toomaj (2017)

Kybernetika

Recently, a new concept of entropy called generalized cumulative entropy of order n was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived...

Generalization of the Kappa coeficient for ordinal categorical data, multiple observers and incomplete designs.

Víctor Abraira, Alberto Pérez de Vargas (1999)

Qüestiió

This paper presents a generalization of the kappa coefficient for multiple observers and incomplete designs. This generalization involves ordinal categorical data and includes weights which permit pondering the severity of disagreement. A generalization for incomplete designs of the kappa coefficient based on explicit definitions of agreement is also proposed. Both generalizations are illustrated with data from a medical diagnosis pilot study.

Generalized information criteria for Bayes decisions

Domingo Morales, Igor Vajda (2012)

Kybernetika

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 α = 1 . It is shown that the most accurate estimate is in this...

Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities

Imre Csiszár, František Matúš (2012)

Kybernetika

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...

Geometría estadística en los espacios de distancia y secuencia: dos aplicaciones.

Eladio Barrio, Celia Buades, Andrés Moya (1992)

Qüestiió

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....

Global information in statistical experiments and consistency of likelihood-based estimates and tests

Igor Vajda (1998)

Kybernetika

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.

Global statistical information in exponential experiments and selection of exponential models

Igor Vajda, E. van der Meulen (1998)

Applications of Mathematics

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.

Goodness of fit tests with weights in the classes based on ( h , φ ) -divergences

Elena Landaburu, Leandro Pardo (2000)

Kybernetika

The aim of the paper is to present a test of goodness of fit with weigths in the classes based on weighted h , φ -divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [frank] and Kapur [kapur]. The weighted h , φ -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...

Goodness-of-fit tests based on K φ -divergence

Teresa Pérez, Julio A. Pardo (2003)

Kybernetika

In this paper a new family of statistics based on K φ -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 φ -divergence.

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