  Linear mixed-effects models are widely used in analyzing clustered or
repeated measures data. We propose a quasi-likelihood approach for estimation
and inference of the unknown parameters in linear mixed-effects models with
high-dimensional fixed effects. The proposed method is applicable to general
settings where the dimension of the random effects and the cluster sizes are
possibly large. Regarding the fixed effects, we provide rate optimal estimators
and valid inference procedures that do not rely on the structural information
of the variance components. We also study the estimation of variance components
with high-dimensional fixed effects in general settings. The algorithms are
easy to implement and computationally fast. The proposed methods are assessed
in various simulation settings and are applied to a real study regarding the
associations between body mass index and genetic polymorphic markers in a
heterogeneous stock mice population.
