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In mixed linear models with nonnormal data, the Gaussian Fisher informationmatrix is called a quasi-information matrix (QUIM). The QUIM plays an importantrole in evaluating the asymptotic covariance matrix of the estimators of themodel parameters, including the variance components. Traditionally, there aretwo ways to estimate the information matrix: the estimated information matrixand the observed one. Because the analytic form of the QUIM involves parametersother than the variance components, for example, the third and fourth momentsof 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 isinconsistent. We propose an estimator of the QUIM that consists partially of anobserved form and partially of an estimated one. We show that this estimator isconsistent and computationally very easy to operate. The method is used toderive large sample tests of statistical hypotheses that involve the variancecomponents in a non-Gaussian mixed linear model. Finite sample performance ofthe test is studied by simulations and compared with the delete-group jackknifemethod that applies to a special case of non-Gaussian mixed linear models.

Partially observed information and inference about non-Gaussian mixed linear models