## Statistics and Applied Probability: A Tribute to Jeffrey J. Hunter

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K. Gustafson, "The Geometry of Statistical Efficiency and Matrix Statistics", *Advances in Decision Sciences*, vol. 2007, Article ID 094515, 16 pages, 2007. https://doi.org/10.1155/2007/94515

# The Geometry of Statistical Efficiency and Matrix Statistics

**Academic Editor:**Paul Cowpertwait

#### Abstract

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.

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#### Copyright

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.