Abstract: Considering the robust estimation problem of linear mixed effect model, a composite quantile regression estimation method based on orthogonal projection is proposed by combining the QR decomposition technique of matrix and the composite quantile regression method. The random effects are eliminated by QR decomposition technique, and then the fixed effects are estimated by constructing the composite quantile regression objective function. Under some regular conditions, the asymptotic normality of the proposed estimates is proved. The proposed estimation method does not need to make any restrictive assumptions about the distribution of model errors and random effects, and the estimates of fixed effects are not affected by random effects. Further, the simulation study compares the proposed method with the orthogonality-based estimation of moment method, which shows that the proposed method is robust and applied to the actual data analysis.

Key words: linear mixed effect model, QR decomposition, composite quantile regression, fixed effect, random effect