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A history of the development of Craig’s theorem. (English) Zbl 0589.62034

Summary: Craig’s theorem [A. T. Craig, Note on the independence of certain quadratic forms. Ann. Math. Stat. 14, 195-197 (1943)] on the independence of quadratic forms in normal variates is traced from its first form, for iid standard normal variates, to the form for variates following an arbitrary nonsingular joint normal distribution. This article gives the main thrust of the development and makes recommendations on coverage of the theorem in courses and textbooks.
The history of Craig’s theorem is not a happy one. The authors of the earlier articles in the literature tended to make errors of a linear- algebraic nature. Authors of more recently published textbooks have given incorrect or misleadingly incomplete coverage of Craig’s theorem and its proof.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas

Citations:

Zbl 0060.308
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