A unified jackknife theory for empirical best prediction with M-estimation

• 成果类型: Article
• 署名作者: Jiang, JM; Lahiri, P; Wan, SM
• 署名单位: University of California System; University of California Davis; University System of Maryland; University of Maryland College Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1043351257
• 发表日期: 2002
• 页码: 1782-1810
• 关键词: small-area estimators; linear mixed models; mean squared error; bayes estimation; inference; samples

摘要

The paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases. The paper develops jackknife theory for the important, but so far neglected, prediction problem for the general mixed model. For estimation of fixed parameters, a jackknife method is considered for a general class of M-estimators which includes the maximum likelihood, residual maximum likelihood and ANOVA estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models. For both the prediction and estimation problems, a jackknife method is used to obtain estimators of the mean squared errors (MSE). Asymptotic unbiasedness of the MSE estimators is shown to hold essentially under certain moment conditions. Simulation studies undertaken support our theoretical results.