孙法省 教授，东北师范大学

Linear mixed model is a popular and common modeling method in statistical analysis. It is computationally difficult to obtain parameter estimates in linear mixed model for big data. The current subsampling methods are mainly aimed at the situation where the data is independent, without considering the correlation within the data. We provide some theoretical results on information matrix for linear mixed model. Based on these findings, an optimal subsampling method for linear mixed model is proposed, which maximizes the determinant of the variance-covariance matrix of the subsampling estimator. Besides, the proposed subsampling procedure is also optimal under A-optimality criterion, which minimizes the trace of the variance-covariance matrix of the subsampling estimator. Furthermore, asymptotic property of the subsampling estimator is established. Numerical examples based on both simulated and real data are provided to illustrate the proposed subsampling method.