The trigonometry of matrix statistics

DOI10.1111/j.1751-5823.2006.tb00169.xMaRDI QIDQ6574124

Karl Gustafson

Publication date: 18 July 2024

Published in: International Statistical Review (Search for Journal in Brave)

zbMATH Keywords

parameter estimationantieigenvalueoperator trigonometrycanonical correlationanti-eigenvectorRayleigh-Ritz theoryWatson statistical efficiency

Mathematics Subject Classification ID

Linear inference, regression (62Jxx) Multivariate analysis (62Hxx) Basic linear algebra (15Axx)

Cites Work

• Matrix versions of the Cauchy and Kantorovich inequalities
• A matrix version of the Wielandt inequality and its applications to statistics
• The geometrical meaning of the Kantorovich-Wielandt inequalities
• Some extensions of the Kantorovich inequality and statistical applications
• A maximization problem and its application to canonical correlation
• Antieigenvalues
• Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor
• On the mathematical foundations of theoretical statistics.
• Interaction antieigenvalues
• Matrix trigonometry
• Operator trigonometry of statistics and econometrics
• Antieigenvalues and antieigenvectors in statistics.
• A note on left multiplication of semigroup generators
• Positive (noncommuting) operator products and semigroups
• Operator trigonometry of the model problem
• On the Calculation of Antieigenvalues and Antieigenvectors
• Inefficiency and correlation
• The inefficiency of least squares
• On the minimum efficiency of least squares
• Differences of means
• The angle of an operator and positive operator products
• An extended operator trigonometry
• Bloomfield-Watson-Knott type inequalities for eigenvalues
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