*On The Degrees of Freedom of Reduced-rank Estimators in*

*Multivariate Regression*

 *Ji Zhu*

 *Department of Statistics*

*University of Michigan*

 *Engr 4201 (CS conference room)*

*4400 University Drive, Fairfax, VA 22030*

*Time: **11**:**0**0 **A**.M. - **12**:**0**0 **P**.M.*

*Date: **Friday**, **Mar 28**, 201**4*


In this project we study the effective degrees of freedom of a general
class of reduced rank estimators for multivariate regression in the
framework of Stein's unbiased risk estimation (SURE). We derive a
finite-sample exact unbiased estimator that admits a closed-form expression
in terms of the singular values or thresholded singular values of the least
squares solution and hence readily computable. The results continue to hold
in the high-dimensional scenario when both the predictor and response
dimensions are allowed to be larger than the sample size. The derived
analytical form facilitates the investigation of its theoretical properties
and provides new insights into the empirical behaviors of the degrees of
freedom. In particular, we examine the differences and connections between
the proposed estimator and a commonly-used naive estimator, i.e., the
number of free parameters. The use of the proposed estimator leads to
efficient and accurate prediction risk estimation and model selection,
as demonstrated
by simulation studies and a data example. This is joint work with Ashin
Mukherjee, Kun Chen and Naisyin Wang.

Yunpeng Zhao, PhD

Assistant Professor
Department of Statistics
Volgenau School of Engineering <[log in to unmask]>
George Mason University
Engineering Building, Room 1719, MS 4A7
4400 University Drive
Fairfax, VA 22030-4444

Phone: 703-993-1674
Email: [log in to unmask]