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Jiang, Jiming; Lahiri, P.; Wan, Shu-Mei

A unified jackknife theory for empirical best prediction with \(M\)-estimation. (English) Zbl 1020.62025

Ann. Stat. 30, No. 6, 1782-1810 (2002).
Summary: 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.

Cited in 1 Review
Cited in 56 Documents

MSC:

62F40 Bootstrap, jackknife and other resampling methods
62G09 Nonparametric statistical resampling methods
62J10 Analysis of variance and covariance (ANOVA)
62J12 Generalized linear models (logistic models)

Keywords:

empirical best predictors; mean squared errors; \(M\)-estimators; mixed linear models; mixed logistic models; small-area estimation; uniform consistency; variance components

Software:

bootstrap
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Full Text: DOI

References:

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