2002/12/01 by Jiming Jiang, Partha Lahiri, Shu‐Mei Wan · 1 citation
Mathematics · #Statistical Methods and Inference #Statistical Methods and Bayesian Inference #Advanced Statistical Methods and Models #Jackknife resampling #Estimator #Mathematics #Moment (physics) #Generalized linear mixed model #Applied mathematics #Linear model #Statistics #Mixed model #Residual #Algorithm
paper · pdf · doi:10.1214/aos/1043351257
openalex publication_date 2002/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.