  This paper introduces a general framework for estimating variance components
in the linear mixed models via general unbiased estimating equations, which
include some well-used estimators such as the restricted maximum likelihood
estimator. We derive the asymptotic covariance matrices and second-order biases
under general estimating equations without assuming the normality of the
underlying distributions and identify a class of second-order unbiased
estimators of variance components. It is also shown that the asymptotic
covariance matrices and second-order biases do not depend on whether the
regression coefficients are estimated by the generalized or ordinary least
squares methods. We carry out numerical studies to check the performance of the
proposed method based on typical linear mixed models.
