A tale of two countries: The Craig-Sakamoto-Matusita theorem

DOI10.1016/j.jspi.2005.09.010zbMath1152.15017OpenAlexW1975155766MaRDI QIDQ947244

Junjiro Ogawa, Ingram Olkin

Publication date: 29 September 2008

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2005.09.010

zbMATH Keywords

quadratic formmatrix equationschi-square distributionCochran's theoremsCraig-Sakamoto-Matusita theorem

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) History of mathematics in the 20th century (01A60) Matrix equations and identities (15A24) Characterization and structure theory of statistical distributions (62E10) History of statistics (62-03) History of linear algebra (15-03) History of Japanese mathematics (01A27)

Related Items (7)

One more simple proof of the Craig-Sakamoto theorem ⋮ A reformulation of the criteria for the independence of quadratic functions in normal variables ⋮ A simple proof of the generalized Craig-Sakamoto theorem ⋮ A generalization of the Craig-Sakamoto theorem to Euclidean Jordan algebras ⋮ An analytical proof of Ogawa's determinantal theorem ⋮ Orthogonal sets of normal or conjugate-normal matrices ⋮ Close to the Craig-Sakamoto's theorem

Cites Work

• On a determinant result of I. Olkin
• An alternative way to establish the necessity part of the classical result on the statistical independence of quadratic forms
• A determinantal proof of the Craig-Sakamoto theorem
• A simple proof of the Craig-Sakamoto theorem
• Craig-Sakamoto's theorem for the Wishart distributions on symmetric cones
• On Craig's theorem and its generalizations
• On the independence of bilinear and quadratic forms of a random sample from a normal population
• On the Stochastic Independence of Two Second-Degree Polynomial Statistics in Normally Distributed Variates
• A History of the Development of Craig's Theorem
• Notes on the distribution of quadratic forms in singular normal variables
• Bilinear Forms in Normally Correlated Variables
• Independence of Non-Negative Quadratic Forms in Normally Correlated Variables
• Independence of Quadratic forms of Normally Correlated Variables
• Pairs of Matrices with Property L
• A Remark on Independence of Linear and Quadratic Forms Involving Independent Gaussian Variables
• Note on the Independence of Certain Quadratic Forms
• Note on a Matric Theorem of A. T. Craig
• Note on the independence of certain statistics
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