**Date & Time:** Tuesday, January 07, 2014, 11:30-12:30.

**Venue:** Ramanujan Hall

**Title:** Estimation of large dimensional covariance and autocovariance matrices

**Speaker:** Arup Bose, ISI Kolkota

**Abstract:** Consider the problem of estimating a covariance matrix when the dimension
is much larger than the sample size. Convergence rates for banded and
tapered estimates is known when the vector observations are independent
and identically distributed (i.i.d.).

We first investigate the case where there is dependence typified by suitable patterned cross covariance structures. These estimators remain consistent in operator norm with appropriate rates of convergence.

Another typical dependent model is the Infinite Dimensional Vector Linear Process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the IVAR process. In that case, we obtain consistent estimators for the parameter matrices. Explicit expression for the estimators are obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large dimensional variance-covariance matrix has the same convergence rate as that in case of i.i.d. samples.