The Geometry of Statistical Efficiency and Matrix Statistics. (13th November 2007)

• Record Type: Journal Article
• Authors: Gustafson, K.
• Other Names: Cowpertwait Paul Academic Editor.
• Is Part Of: Journal of applied mathematics & decision sciences. Volume 2007(2007)
• Publication Date: 2007-11-13
• Subjects: Operations research -- Periodicals; Mathematical models -- Periodicals; Statistics -- Periodicals; Quality control -- Periodicals; Mathematical models; Operations research; Quality control; Statistics; Periodicals; 519.05
• DOI: 10.1155/2007/94515
• Languages: English
• ISSNs: 1173-9126

Abstract

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.