of dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TOTAL BREGMAN DIVERGENCE, A ROBUST DIVERGENCE MEASURE, AND ITS APPLICATIONS By Meizhu Liu December 2011 Chair: Baba C. Vemuri Major: Computer Engineering Divergence measures provide a means to measure the pairwise dissimilarity between “...

The Akaike information criterion, AIC, is a widely known and extensively used tool for statistical model selection. AIC serves as an asymptotically unbiased estimator of a variant of Kullback's directed divergence between the true model and a tted approximating model. The directed divergence is an asymmetric measure of separation between two statistical models, meaning that an alternate directe...

In this paper we study polytomous logistic regression model and the asymptotic properties of the minimum φ-divergence estimators for this model. A simulation study is conducted to analyze the behavior of these estimators as function of the power-divergence measure φ(λ). AMS 2001 Subject Classification Primary 62H15 · Secondary 62H17

In this paper we have considered two one parametric generalizations. These two generalizations have in particular the well known measures such as: J-divergence, Jensen-Shannon divergence and arithmetic-geometric mean divergence. These three measures are with logarithmic expressions. Also, we have particular cases the measures such as: Hellinger discrimination, symmetric χ2−divergence, and trian...

As early as in 1952, Chernoff 1 used the α-divergence to evaluate classification errors. Since then, the study of various divergence measures has been attracting many researchers. So far, we have known that the Csiszár f-divergence is a unique class of divergences having information monotonicity, from which the dual α geometrical structure with the Fisher metric is derived, and the Bregman dive...

Given a finitely connected planar Jordan domain Ω, it is possible to define a divergence distance D(x, y) from x ∈ Ω to y ∈ Ω, which takes into account the complex geometry of the domain. This distance function is based on the concept of f -divergence, a distance measure traditionally used to measure the difference between two probability distributions. The relevant probability distributions in...

When testing for discriminating between two competing models, a statistical method, usually, proceeds by evaluating the measure for discrepancy between the observed data and each parametric model. The parameter model with smaller value of measure statistic is generally chosen. This paper addresses the question of testing for choosing between two estimated models using some φ−divergence type sta...

This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many applications to establish a proper data average. The main purpose is to widen the range of possible interpretations and relations of the Fisher distance and its a...

Suggested molecular mechanisms for the generation of new tandem repeats of simple sequences indicate that the microsatellite loci evolve via some of forward-backward mutation. We provide a mathematical basis for suggesting a measure of genetic distance between populations based on microsatellite variation. Our results indicate that such a genetic distance measure can remain proportional to the ...

This paper concerns the approximation of probability measures on Rd with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this divergence, from certain sets of Gaussian measures and Gaussian mixtures. The asymptotic behavior of such best approximations is then studied in the frequently occuring small...