Operator trigonometry of statistics and econometrics

A new and useful geometric point of view for the understanding and analysis of certain matrix methods as they are used in statistics and econometrics is presented. Applications to statistical efficiency, parameter estimation, and correlation theory are given. In particular we show that worst case relative least squares efficiency, although achieved by maximally inefficient regressors, is also achieved by maximal covariance matrix turning vectors. Also we elaborate geometrically a commutator trace efficiency result of P. Bloomfield and G.S. Watson [Biometrika 62 (1975) 121]. Well-established Lagrange multiplier methods for constrained optimizations are compared to use of an Euler equation from the new geometric theory. (C) 2002 Elsevier Science Inc. All rights reserved.