13 February 2012
We hope you can join us this Wednesday, February 15, 2012 for the Applied Statistics Workshop. Tamar Sofer, a Ph.D. student from the Department of Biostatistics at Harvard University, will give a presentation entitled "Sparse Joint Estimation of Covariates-Dependent Covariance Matrices". A light lunch will be served at 12 pm and the talk will begin at 12.15.
"Sparse Joint Estimation of Covariates-Dependent Covariance Matrices"
Department of Biostatistics, Harvard University
CGIS K354 (1737 Cambridge St.)
Wednesday, February 15th, 2012 12.00 pm
We propose an estimation method for the principal components/covariance structures of a set of outcomes, while modeling the effect of covariates. We assume a linear mixed model formulation on the outcomes as response to covariates, a model corresponding to spiked covariance matrices. Since the subject-specific covariance matrices and the effects of covariates are believed to be sparse, we penalize coefficients using an oracle penalty function. Under some assumptions on the parameters and the likelihood, we show that the maximum likelihood estimator of the parameters is asymptotically consistent and is uniformly sparse ("sparsistent"), even when the number of parameters is small. We propose using the Bayesian Information Criterion (BIC) for tuning parameter selection and show that it is consistent for model selection. Using a simple iterated least squares procedure we are able to recover the model parameters with high accuracy. The method is implemented to study the effect of smoking on the covariances of gene methylations in the asthma pathway in smokers and non-smokers US veterans from the Normative Aging Study (NAS).