Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 94515, 16 pages
Review Article

The Geometry of Statistical Efficiency and Matrix Statistics

K. Gustafson

Department of Mathematics, University of Colorado at Boulder, Boulder 80309, Colo, USA

Received 23 March 2007; Accepted 8 August 2007

Academic Editor: Paul Cowpertwait

Copyright © 2007 K. Gustafson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We will place certain parts of the theory of statistical efficiency into the author's operator trigonometry (1967), thereby providing new geometrical understanding of statistical efficiency. Important earlier results of Bloomfield and Watson, Durbin and Kendall, Rao and Rao, will be so interpreted. For example, worse case relative least squares efficiency corresponds to and is achieved by the maximal turning antieigenvectors of the covariance matrix. Some little-known historical perspectives will also be exposed. The overall view will be emphasized.