APPROXIMATIONS FOR DENSITIES OF SUFFICIENT-ESTIMATORS
成果类型：
Article
署名作者：
DURBIN, J
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/67.2.311
发表日期：
1980
页码：
311333
关键词：
摘要：
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 and Cox (1979) for exponential families. A series expansion in powers of n-1 is derived of which the 1st term has an error of order n-1 which can effectively be reduced to n-3/2 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.
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