Skip Navigation

Correction for BEHBOODIAN, Biometrika 57 (1) 215-217.
Biometrika 1970 57(1):224; doi:10.1093/biomet/57.1.224-a
© 1970 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

CORRECTIONS

Corrections

The main result was that if x ~ N(0,C), then x'Ax has a chi-squared if and only if the eigenvalues of AC are all 0 or 1. The three corollaries were then intended to be in part contributions to matrix theory, but Dr D.N.Shanbhag and Dr G.P.H. Styan have kindy pointed out that the ‘necessary’ parts of Corollaries (i) and (ii) are incorrect was incorrect. Also I misquoted one of Shanbhag's results by writing ‘rant’ in place of ‘trace’. He proved that if AC is symmetric then the criteria of Corollary (i) are valid; a fact that I stated ambiguously.

The error made in the proof of Corollary (ii) was in the assumption that the rank of a matrix B is equal to the number of its nonzero eigenvalues. In fact it is equal to the number of its nonzero ‘singular’ values, which are the square roots of the nonzero eigenvalues of BB'. It is correctly, but only implicitly assumed that AC has real eigenvalues when A and C are real and symmetric and one of them is non-negative definite; see, for example, p.378 of Good [J. R. Statist. Soc. B 25 (1963), 377–82; Corrigenda 28 (1966), 584].


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.