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Operator trigonometry of statistics and econometrics. (English) Zbl 1015.62054

Summary: 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, 121-128 (1975; Zbl 0308.62056)]. Well-established Lagrange multiplier methods for constrained optimization are compared to the use of Euler equations from the new geometric theory.

MSC:

62H12 Estimation in multivariate analysis
15A99 Basic linear algebra
62J05 Linear regression; mixed models
62A01 Foundations and philosophical topics in statistics

Citations:

Zbl 0308.62056
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