Geodesic Estimation in Elliptical Distributions

✍ Scribed by Maia Berkane; Kevin Oden; Peter M. Bentler

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 318 KB
• Volume: 63
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1997.1690

✦ Synopsis

face very complicated systems of differential equations characterizing the geodesic curves. In general, no closed form solutions for these systems are available. In this paper, we investigate the class of multivariate elliptical distributions. We find that a change of coordinates reduces the system of geodesic equations to a very simple form admitting an appealing solution that is nothing but a straight line. The distance between two elliptical distributions with equal location and different scatter matrices is then calculated. This geodesic distance which is based on the information metric, comes as an addition to the list of geodesic distances given by Rao (1987). We then derive a geodesic discrepancy function for use in covariance structure analysis. The estimator of the structure parameter is shown to have desirable properties. A test statistic is then built upon this discrepancy function and shown to be asymptotically distributed as / 2 .