Advances in Decision Sciences
Volume 2007 (2007), Article ID 94515, 16 pages
doi:10.1155/2007/94515

The geometry of statistical efficiency and matrix statistics

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.