A Generalized φ-Divergence for Asymptotically Multivariate Normal Models

Selected Estimated Models with Φ−divergence Statistics

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...

Screening for a Multivariate Mixture Normal Distribution

Kullback-Leibler Divergence Measure for Multivariate Skew-Normal Distributions

The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these...

Strong Convergence Theorem for Fixed Points of Nearly Uniformly L−Lipschitzian Asymptotically Generalized Φ-Hemicontractive Mappings

Let C be a nonempty convex subset of a real Banach space E in which the normalized duality map is norm-to-norm uniformly continuous on bounded subsets of E. Let T be a nearly uniformly L−Lipschitzian asymptotically generalized Φ-hemicontractive map in the intermediate sense. An iterative process of the Manntype is proved to converge strongly to the unique fixed point of T . Under this setting, ...

Minimum Φ-divergence Estimator and Hierarchical Testing in Loglinear Models

In this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum φ-divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a φ-divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the prob...