- Series
- Stochastics Seminar
- Time
- Thursday, January 26, 2017 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles006
- Speaker
- Vladimir Koltchinskii – Georgia Tech
- Organizer
- Christian Houdré
We study the problem of estimation of a linear functional of the eigenvector
of covariance
operator that corresponds to its largest eigenvalue (the first principal
component) based
on i.i.d. sample of centered Gaussian observations with this covariance. The
problem is studied
in a dimension-free framework with its complexity being characterized by so
called "effective rank"
of the true covariance. In this framework, we establish a minimax lower
bound on the mean squared
error of estimation of linear functional and construct an asymptotically
normal
estimator for which the bound is attained. The standard "naive" estimator
(the linear functional
of the empirical principal component) is suboptimal in this problem.
The talk is based on a joint work with Richard Nickl.