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: 11:00 A.M. - 12:00 P.M.

Date: Friday, Mar 28, 2014 


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
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]