Estimation for High‐Dimensional Linear Mixed‐Effects Models Using ℓ1‐Penalization
By Jürg Schelldorfer, Peter Buhlmann, S. De Geer. 2010
185 citations recorded by the source corpus.
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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/142844416c96f20070a12c153272c6e31f837537
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Statistics and Probability
- Peter Buhlmann
- Markus Kalisch
- Lukas Meier
- Samuel Müller
- Nicolai Meinshausen
- Sara A. van de Geer
- Jean Daunizeau
- Janice L. Scealy
Citations in the corpus
- High-Dimensional Statistics with a View Toward Applications in Biology (2014, methodology): “…using the Laplace approximation as used in Schelldorfer et al. (2013); the former causes generic computational difficulties as well as more subtle conditions and arguments to establish good properties of the estimator as discussed in Schelldorfer et al. (2011) for Gaussian linear mixed models.”
- GLMix: Generalized Linear Mixed Models For Large-Scale Response Prediction (2016, methodology): “[20] used BCD for a mixed effects model that contains only the scalar random effects for Gaussian responses.”
- Bayesian mixed-effects inference on classification performance in hierarchical data sets (2012, background): “For instance, Schelldorfer et al. (2011) proposed a linear mixed-effects model for classification that accounts for different sources of variation in the data.”
- Model Selection in Linear Mixed Models (2013, methodology): “Notice that the parameters γ are selected in a grouped manner similar to the LASSO for grouped variables (Yuan and Lin (2006)), and this helps preserve the positive definite constraint in Ψ. Bondell, Krishna and Ghosh (2010) use the alternative Cholesky factor parametrization Γi = σD † iΓ † i , wher”