Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families
本文探讨了基于鞍点方法的高阶渐近性在多参数指数族（尤其是广义线性模型）中的实际应用，通过调整似然比统计量的符号平方根来近似精确条件推断，并区分了两种调整：减少冗余参数估计的影响和调整感兴趣参数信息不足的问题。
SUMMARY Recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families, especially in generalized linear models. The aim here is to clarify and explore these. Attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family. Excellent approximations to exact conditional inferences are often available, in terms of simple adjustments to the signed square root of the likelihood ratio statistic. The focus is on distinguishing between two aspects of the adjustments: one reducing effects of nuisance parameter estimation and the other adjusting for little information regarding the parameter of interest. Numerical results are given for some Poisson and multinomial models.