Statistics and Data Science Seminar
Dr. XiaoHui Chen
The University of British Columbia
Covariance and Precision Matrix Estimation for High-Dimensional Time Series
Abstract: Covariance matrix and its inverse (a.k.a. precision matrix) play a central role in a
broad range of problems in statistics and machine learning. In the past few years, there
has been an explosion of interest in regularized covariance and precision matrix
estimation for high-dimensional i.i.d. random vectors with sub-Gaussian tails.
In this talk, we shall discuss the estimation of covariance and precision matrices
for stationary and locally stationary high-dimensional time series. In the latter case,
the covariance matrices evolve smoothly in time and thus form a covariance matrix
function. Under the framework of Wu (2005)'s functional dependence measure, we obtain
the rate of convergence for the thresholded covariance matrix estimate and illustrate
how the dependence affects the rate of convergence. Asymptotic properties are also
obtained for the precision matrix estimate based on the graphical Lasso principle.
Our theory substantially generalizes earlier ones by allowing dependence, by allowing
non-stationarity and by relaxing the associated moment conditions. Our new results
have implications on a number of classical problems, including spatial-temporal
statistics and graphical models, among many others.
Wednesday October 3, 2012 at 4:00 PM in SEO 636