Approximations for Densities of Sufficient Estimators
本文提出一种简单方法，用于获得充分估计量密度的渐近展开式，扩展了Barndorff-Nielsen & Cox对指数族的方法，并证明了多元Edgeworth展开在参数统计族中的有效性，适用于时间序列分析等问题。
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−1 which 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.