Skip Navigation

Biometrika 1984 71(3):461-476; doi:10.1093/biomet/71.3.461
© 1984 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 Articles by McCULLAGH, P.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Tensor notation and cumulants of polynomials

PETER McCULLAGH

Department of Mathematics, Imperial College London, U.K.

A modified and extended tensor notation is introduced that is sufficient to cover multivariate moments and cumulants as special cases. Using this notation, two basic identities are given. The first of these expresses generalized cumulants in terms of ordinary cumulants. The second gives the joint cumulant generating function of any polynomial transformation in terms of the cumulants of the original variables. Three applications of the basic identities are given. The first application is concerned with sample cumulants or k-statistics, the second to Edgeworth series and the third to exponential family models.

Key Words: Bartlett correction factor • Cumulant • Cumulant tensor • Edgeworth series • Exponential family • Generalized cumulant • Graph • Hermite tensor • k-statistic • Möbius function • Partition lattice • Pattern function • Polynomial transformation • Signed likelihood ratio statistic • Tensor


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.