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December 2005 Partially observed information and inference about non-Gaussian mixed linear models
Jiming Jiang
Ann. Statist. 33(6): 2695-2731 (December 2005). DOI: 10.1214/009053605000000543


In mixed linear models with nonnormal data, the Gaussian Fisher information matrix is called a quasi-information matrix (QUIM). The QUIM plays an important role in evaluating the asymptotic covariance matrix of the estimators of the model parameters, including the variance components. Traditionally, there are two ways to estimate the information matrix: the estimated information matrix and the observed one. Because the analytic form of the QUIM involves parameters other than the variance components, for example, the third and fourth moments of the random effects, the estimated QUIM is not available. On the other hand, because of the dependence and nonnormality of the data, the observed QUIM is inconsistent. We propose an estimator of the QUIM that consists partially of an observed form and partially of an estimated one. We show that this estimator is consistent and computationally very easy to operate. The method is used to derive large sample tests of statistical hypotheses that involve the variance components in a non-Gaussian mixed linear model. Finite sample performance of the test is studied by simulations and compared with the delete-group jackknife method that applies to a special case of non-Gaussian mixed linear models.


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Jiming Jiang. "Partially observed information and inference about non-Gaussian mixed linear models." Ann. Statist. 33 (6) 2695 - 2731, December 2005.


Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1084.62060
MathSciNet: MR2253099
Digital Object Identifier: 10.1214/009053605000000543

Primary: 62B99 , 62J99

Keywords: asymptotic covariance matrix , dispersion tests , estimated information , nonnormal mixed linear model , observed information , POQUIM , quasi-likelihood , REML

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 6 • December 2005
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