In this paper we consider an exploratory canonical analysis approach for multinomial population based on the (^-divergence measure. We define the restricted minimum 4>divergence estimator, which is seen to be a generalization of the restricted maximum likeli­ hood estimator. This estimator is then used in ^-divergence goodness-of-fit statistics which is the basis of two new families of statisti...

In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We provide an in-depth study of the quantum skew divergence, including its relation to other state distinguishability measures. Finally, we present a number of important applications: new continuity i...

The fitness consequences of inbreeding and outbreeding have intrigued biologists for a long time. Recently a measure of relatedness of parental haplotypes has been proposed called mean d(2). This measure is based on a stepwise mutational process and therefore is tailored to microsatellite genetic markers. Theoretical work suggests that mean d(2) typically is less suited for measuring fitness co...

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy, a Bregman distance, or an f -divergence....

Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon’s entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its order. In particular, the Rényi divergence of order 1 equals the Kullback-Leibl...

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy, a Bregman distance, or an f -divergence....

This paper generalizes the nonparametric approach to option pricing of Stutzer (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie-Read family of divergence measures. While the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the abilit...

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 “...

This paper proposes and evaluates a new statistical discrimination measure for hidden Markov models (HMMs) extending the notion of divergence [1], a measure of average discrimination information originally defined for two probability density functions. The Average Divergence Distance (ADD) is proposed as a statistical discrimination measure between two HMMs, considering the transient behavior o...