Accession Number : ADA186385
Title : The Information Metric for Univariate Linear Elliptic Models.
Descriptive Note : Technical rept.,
Corporate Author : PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS
Personal Author(s) : Burbea, Jacob ; Oller, Jose M
PDF Url : ADA186385
Report Date : Jun 1987
Pagination or Media Count : 21
Abstract : THe concepts of metrics and distances are fundamental in problems of statistical inference and in practical applications to study affinities among a given set of populations. A statistical model is specified by a family of probability distributions, described by a set of continuous parameters known as the parameter space. This model possesses some geometrical properties which are induced by the local information structures of the distributions. In particular, the Fisher information matrix of the given family of distributions gives rise to a Riemannian metric over the parameter space, whose geodesic distance, known as the Rao distance, plays a major role in the multivariate statistical techniques. For the family of multivariate normal distributions with fixed shape but varying locations, this distance reduces the well-known Mahalanobis distance. This document refers to Burbea and Rao for more details on these concepts and their derivations. An interesting statistical model is provided by the family of elliptic distributions whose density functions have elliptical contours and which include the multivariate normal distributions as a subfamily. This paper studies the information metric associated with an elliptic family whose shape varies linearly.
Descriptors : *MATHEMATICAL MODELS, *STATISTICAL INFERENCE, *METRIC SYSTEM, CONTOURS, DENSITY, ELLIPSES, GEODESICS, GEOMETRY, LINEARITY, MULTIVARIATE ANALYSIS, NORMAL DISTRIBUTION, PROBABILITY DISTRIBUTION FUNCTIONS, RANGE(DISTANCE), SHAPE, STATISTICAL ANALYSIS, STATISTICAL PROCESSES, VARIATIONS, POPULATION(MATHEMATICS)
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE