Skip Navigation

Biometrika 1980 67(2):311-333; doi:10.1093/biomet/67.2.311
© 1980 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 DURBIN, J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Approximations for densities of sufficient estimators

J. DURBIN

Department of Statistics, London School of Economics and Political Science

A simple method of obtaining asymptotic expansions for the densities of sufficient estimators is described. It is an extension of the one developed by Barndorff-Nielsen & Cox (1979) for exponential families. A series expansion in powers of n–1 is derived of which the first term has an error of order n–1which can effectively be reduced to n– / by renormalization.The results obtained are similar to those given by Daniels's (1954) saddlepoint method but the derivations are simpler. A brief treatment of approximations to conditional densities is given. Theorems are proved which extend the validity of the multivariate Edgeworth expansion to parametric families of densities of statistics which need not be standardized sums of independent and identically distributed vectors. These extensions permit the treatment of problems arising in time series analysis. The technique is used in another paper (Durbin, 1980) to obtain approximations to the densities of partial serial correlation coefficients.

Key Words: Asymptotic expansion • Circular autoregressive process • Conditional density • Edgeworth series • Saddlepoint approximation • Time series.


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.