Moment information and entropy evaluation for probability densities

How much information does the sequence of integer moments carry about the corresponding unknown absolutely continuous distribution? We prove that a reliable evaluation of the corresponding Shannon entropy can be done by exploiting some known theoretical results on the entropy convergence, uniquely involving exact moments without solving the underlying moment problem. All the procedure essentially rests on the solution of linear systems, with nearly singular matrices, and hence it requires both calculations in high precision and a pre-conditioning technique. Numerical examples are provided to support the theoretical results.     

Information Measure in Terms of the Hazard Function and Its Estimate

It is well-known that some information measures, including Fisher information and entropy, can be represented in terms of the hazard function. In this paper, we provide the representations of more information measures, including quantal Fisher information and quantal Kullback-leibler information, in terms of the hazard function and reverse hazard function. We provide some estimators of the quantal KL information, which include the Anderson-Darling test statistic, and compare their performances.     

Jensen-Shannon divergence in conjugate spaces: The entropy excess of atomic systems and sets with respect to their constituents

The disorder of a composite system or of a set of different systems is always higher than the mere sum of the internal disorder of its constituents. One of the most widely used functionals employed for measuring the randomness of a single distribution is the Shannon entropy, from which the increase of disorder within the composite system with respect to those of the constituents is quantified by means of the Jensen-Shannon Divergence (JSD). In this work two different applications of the JSD in the study of the information content of atomic electron densities are carried out: (i) finding the contribution for a given atom of its composing subshells to the total atomic information; (ii) and similarly for selected sets of atoms, such as periods and groups throughout the Periodic Table as well as isoelectronic series. In both cases, the analysis is performed in the two conjugate position and momentum spaces, and the results are interpreted according to physically relevant quantities such as the ionization potential.     

A minimum discrimination information estimator of preliminary conjectured normal variance

For the problem of estimating the normal variance ² based on random sampleX ₁,...,X _n when a preliminary conjectured interval [C ₀ ^–1 ₀ ² ,C _{0 0} ² ] is available, the minimum discrimination information (MDI) approach is presented. This provides a simple way of specifying the prior information, and also allows to consider a shrinkage type estimator. MDI estimator and its mean square error are derived. The estimator compares favorably with the previously proposed estimators in terms of mean square error efficiency.     

ASSESSING LOCAL PRIOR INFLUENCE IN BAYESIAN ANALYSIS

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BAYESIAN LOCAL INFLUENCE ASSESSMENTS IN A GROWTH CURVE MODEL WITH GENERAL COVARIANCE STRUCTURE

1 IntroductionThe problem of how to deal With local influence assessment in a growth curve model withgeneral covariance structure is very important. There are two main reasons why this is so. First,although the growth curve model can be viewed as a generalizetion of classical linear regressionmodel in some wad, as pointed out by for etc.[1], two models are substantially different andthe former is much more complicated than the latter. Secondly3 it is not generally the case withlocally influen…     

Estimating a model through the conditional MLE

The estimation problem of a model through the conditional maximum likelihood estimator (MLE) is explored. The estimated model is compared using the two dual Kullback-Leibler losses with that through the unconditional MLE. The former is found to be superior to the latter under familiar models. This result is applicable to the model selection problem. These suggest a novel extensive use of the conditional likelihood, since the traditional use of the conditional likelihood was restricted only on inference for the structural parameter.     

A classification of the main probability distributions by minimizing the weighted logarithmic measure of deviation

The paper reanalyzes the following nonlinear program: Find the most similar probability distribution to a given reference measure subject to constraints expressed by mean values by minimizing the weighted logarithmic deviation. The main probability distributions are examined from this point of view and the results are summarized in a table.The author acknowledges the NSERC Canada Research Grant A-5712.     

RESAMPLING TESTS OF STATISTICAL HYPOTHESES

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