On Properties of Predictive Priors in Linear Models

Utilizing the notion of matching predictives as in Berger and Pericchi, we show that for the conjugate family of prior distributions in the normal linear model, the symmetric Kullback-Leibler divergence between two particular predictive densities is minimized when the prior hyperparameters are taken to be those corresponding to the predictive priors proposed in Ibrahim and Laud and Laud and Ibrahim. The main application for this result is for Bayesian variable selection.     

On entropy of a Pareto distribution in the presence of outliers

ABSTRACT

The aim of this paper is obtaining the amount of information there exists in the Pareto distribution in the presence of outliers. For the sake of this purpose, Shannon entropy, ?-entropy, Fisher information, and Kullback–Leibler distance are computed. Furthermore, a section has been devoted to compare these quantities in these two cases of the Pareto distribution (with outliers and the homogenous case). At the end of this paper, two actual examples, which are related to insurance companies, are brought. A brief summary of which is done in this work is also reported.     

Mutual information as a measure of multivariate association: analytical properties and statistical estimation

Mutual information (also known as Kullback–Leibler divergence) can be viewed as a measure of multivariate association in a random vector. The definition incorporates the joint density as well as the marginal densities. We will focus on a representation of mutual information in terms of copula densities that is thus independent of the marginal distributions. This representation yields a different approach to estimating mutual information than the original definition does, as only the copula density has to be estimated. We review analytical properties and examples for selected distributions and discuss methods of nonparametric estimation of copula densities and hence of the mutual information from a sample. Based on a simulation study, we compare the performance of these estimators with respect to bias, standard deviation, and the root mean squared error. The Gauss and the Frank copula are considered as examples.     

Comparison of the Iterative Stein-Rule and the Usual Estimators of the Disturbance Variance Under the Pitman Nearness Criterion in a Linear Regression Model with Proxy Variables

In a linear regression model with proxy variables, the iterative Stein-rule estimator and the usual estimator of the disturbance variance is compared under the Pitman Nearness Criterion. The exact expression of Pitman Nearness probability is derived and numerically evaluated.