Likelihood for statistically equivalent models

• 成果类型: Article
• 署名作者: Copas, John; Eguchi, Shinto
• 署名单位: University of Warwick; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2009.00732.x
• 发表日期: 2010
• 页码: 193-217
• 关键词: selection

摘要

In likelihood inference we usually assume that the model is fixed and then base inference on the corresponding likelihood function. Often, however, the choice of model is rather arbitrary, and there may be other models which fit the data equally well. We study robustness of likelihood inference over such 'statistically equivalent' models and suggest a simple 'envelope likelihood' to capture this aspect of model uncertainty. Robustness depends critically on how we specify the parameter of interest. Some asymptotic theory is presented, illustrated by three examples.