PRACTICAL USE OF HIGHER-ORDER ASYMPTOTICS FOR MULTIPARAMETER EXPONENTIAL-FAMILIES

• 成果类型: Article
• 署名作者: PIERCE, DA; PETERS, D
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• 发表日期: 1992
• 页码: 701-737
• 关键词: log likelihood ratio; approximate interval probabilities; independent random-variables; marginal tail probabilities; saddle-point approximation; conditional inference; odds ratio; scalar parameters; distributions; estimators

摘要

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.