Abstract. We propose an ℓ1-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, that is, for clustered data. We prove a consistency and an oracle optimality result and we develop an algorithm with provable numerical convergence. Furthermore, we demonstrate the performance of the method on simulated and a real high-dimensional data set.
%0 Journal Article
%1 schelldorfer_estimation_2011
%A Schelldorfer, Jürg
%A Bühlmann, Peter
%A De Geer, Sara Van
%D 2011
%J Scandinavian Journal of Statistics
%K LASSO, Lasso, adaptive components coordinate coordinatewise descent, effects, gradient optimization, random selection, variable variance
%N 2
%P 197--214
%R 10.1111/j.1467-9469.2011.00740.x
%T Estimation for high-dimensional linear mixed-effects models using ℓ1-penalization
%U http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9469.2011.00740.x/abstract
%V 38
%X Abstract. We propose an ℓ1-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, that is, for clustered data. We prove a consistency and an oracle optimality result and we develop an algorithm with provable numerical convergence. Furthermore, we demonstrate the performance of the method on simulated and a real high-dimensional data set.