Dear all,
Please join us for the Applied Statistics Workshop (Gov 3009) this
Wednesday, February 15 from 12.00 - 1.30 pm in CGIS Knafel Room 354. 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". As always, a light lunch will be
provided.
Abstract:
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).
An up-to-date schedule for the workshop is available at
http://www.iq.harvard.edu/events/node/1208.
Best,
Konstantin
--
Konstantin Kashin
Ph.D. Student in Government
Harvard University
Mobile: 978-844-0538
E-mail: kkashin(a)fas.harvard.edu
Site:
http://people.fas.harvard.edu/~kkashin/