NONREGULAR MAXIMUM-LIKELIHOOD PROBLEMS

• 成果类型: Article
• 署名作者: CHENG, RCH; TRAYLOR, L
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• 发表日期: 1995
• 页码: 3-44
• 关键词: normal mixture; ratio tests; threshold autoregression; percentage points; constant hazard; models; inference; parameter; EXISTENCE; densities

摘要

Four non-regular estimation problems are reviewed and discussed. One (the unbounded likelihood problem) involves distributions with infinite spikes, for which maximum likelihood can fail to give consistent estimators. A comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case. An application to the Box-Cox shifted power transform is given. The other three problems occur when the true parameter lies in some special subregion. In one (the constrained parameter problem) the subregion is a boundary. The other two (the embedded model and the indeterminate parameters problems) occur when the model takes on a special form in the subregion. These last two problems have previously been investigated separately. We show that they are equivalent in some situations. Both often arise in non-linear models and we give a directed graph approach which allows for their occurrence in nested model building. It is argued that many non-regular problems can be handled systematically without having to resort to elaborate technical assumptions. Relatively uncomplicated methods may be used provided that the underlying nature of the non-regularity is understood.