POTENTIAL FUNCTIONS AND CONSERVATIVE ESTIMATING FUNCTIONS

• 成果类型: Article
• 署名作者: LI, B; MCCULLAGH, P
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325372
• 发表日期: 1994
• 页码: 340-356
• 关键词: quasi-likelihood functions; models

摘要

A quasiscore function, as defined by Wedderbum and by McCullagh, frequently fails to have a symmetric derivative matrix Such a score function cannot be the gradient Of any Potential function on the parameter space; that is, there is no ''quasilikelihood.'' Without a likelihood function it is difficult to distinguish good roots from bad roots or to set satisfactory confidence limits. From a different perspective, a potential function seems to be essential in order to give the theory an approximate Bayesian interpretation. The purpose of this paper is to satisfy these needs by developing a method of projecting the true score function onto a class of conservative estimating functions. By construction, a potential function for the projected score exists having many properties of a log-likelihood function.