A Family of Measures of Uncertainty Involving Utilities: Definition, Properties, Applications and Statistical Inferences.
A general class of entropy statistics
To study the asymptotic properties of entropy estimates, we use a unified expression, called the -entropy. Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators are considered, so they can be used to construct confidence intervals and to test statistical hypotheses based on one or more samples. These results can also be applied to multinomial populations.
A method of detecting changes in the behaviour of locally stationary sequences
A new approach to mutual information
A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
A new approach to mutual information. II
A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.
A note on quantifying the uncertainty corresponding to the utilities.
In a previous paper we have studied the relevant analogies between the variance, applied to a compound scheme of probability and utility, and the measure which we had defined to evaluate the unquietness for such a compound scheme.The purpose of the present note is to display the advantage exhibited by the second measure, with respect to the first one, in quantifying the uncertainty corresponding to the utilities. This advantage consists of the larger ability to distinguish among the different compound...
A stronger version of matrix convexity as applied to functions of Hermitian matrices.
A summary on entropy statistics
About the maximum information and maximum likelihood principles
Neural networks with radial basis functions are considered, and the Shannon information in their output concerning input. The role of information- preserving input transformations is discussed when the network is specified by the maximum information principle and by the maximum likelihood principle. A transformation is found which simplifies the input structure in the sense that it minimizes the entropy in the class of all information-preserving transformations. Such transformation need not be unique...
Adaptive tests for periodic signal detection with applications to laser vibrometry
Initially motivated by a practical issue in target detection via laser vibrometry, we are interested in the problem of periodic signal detection in a Gaussian fixed design regression framework. Assuming that the signal belongs to some periodic Sobolev ball and that the variance of the noise is known, we first consider the problem from a minimax point of view: we evaluate the so-called minimax separation rate which corresponds to the minimal l2-distance between the signal and zero so that the detection...
Algunas consideraciones sobre la información generalizada.
De Groot ha definido una medida de información que generaliza la información de Kullback como medida de discrepancia entre dos distribuciones.En el presente artículo definimos la información modal, como caso particular de la información generalizada, la cual servirá para demostrar que las principales propiedades de la información de Kullback no se verifican para la medida dada por De Groot.
An exploratory canonical analysis approach for multinomial populations based on the -divergence measure
In this paper we consider an exploratory canonical analysis approach for multinomial population based on the -divergence measure. We define the restricted minimum -divergence estimator, which is seen to be a generalization of the restricted maximum likelihood estimator. This estimator is then used in -divergence goodness-of-fit statistics which is the basis of two new families of statistics for solving the problem of selecting the number of significant correlations as well as the appropriateness...
An index of diversity in stratified random sampling based on the hypoentropy measure.
We consider a measure of the diversity of a population based on the λ-measure of hypoentropy introduced by Ferreri (1980). Our purpose is to study its asymptotic distribution in a stratified sampling and its application to testing hypothesis. A numerical example based on real data is given.
Análisis de distribuciones a priori bajo cierta información parcial.
Se calculan las distribuciones menos informativas cuando se utilizan como medidas de información la entropía útil y la energía informacional de Onicescu, tanto si el espacio de estados Θ es continuo (intervalo de R) como si es discreto y suponiendo que el decisor posee información acerca de algunas características de la distribución a priori (monotonías de la función de densidad, probabilidades de subconjuntos de Θ, monotonías o cotas de la razón de fallo).
Analysis of a measurement information
Analysis of FM demodulator output noise with applications to FM telemetry.
Approximating Fisher's information for the replicated linear circular functional relationship model.
Asymptotic behaviour of an estimator based on Rao's divergence
Asymptotic behaviour of empirical multiinformation
Asymptotic distribution of the useful informational energy