American Statistical Association
The selection of random effects in linear mixed models is an important yet challenging problem in practice. We propose a robust and unified framework for automatically selecting random effects and estimating covariance components in linear mixed models. A moment-based loss function is first constructed for estimating the covariance matrix of random effects. Two types of shrinkage penalties, a hard-thresholding operator and a new sandwich-type soft-thresholding penalty, are then imposed for sparse estimation and random effects selection. Compared with existing approaches, the new procedure does not require any distributional assumption on the random effects and error terms. We establish the asymptotic properties of the resulting estimator in terms of its consistency for both random effects selection and variance component estimation. Optimization strategies are suggested to tackle the computational challenges involved in estimating the sparse variance-covariance matrix. Furthermore, we extend the procedure to incorporate the selection of fixed effects as well. Numerical studies show promising performance of the new approach in selecting both random and fixed effects and estimating model parameters. Finally, we apply the approach to a data set from the Amsterdam Growth and Health study.
Dr. Wenbin Lu received is doctoral degree in Statistics from Columbia University in 2003. He then joined the Statistics Department in NCSU. His research interests include survival analysis, semiparametric methods, high dimensional data analysis, statistical methods for personalized treatments and statistical genetics. His current research is partly supported by several NIH grants. He is an associate editor for Biostatistics and Journal of Statistical Theory and Practice.
|Date:||Thursday, September 22, 2011|
|Time:||4:00 - 5:00 P.M.|
Mailman School of Public Health
Department of Biostatistics
722 West 168th Street
Biostatistics Computer Lab
6th Floor - Room 656
New York, New York