Degrees of Freedom of the Reduced Rank Regression

• Activity Number: 568
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Ashin Mukherjee*+ and Ji Zhu and Naisyin Wang
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Degrees of Freedom ; Reduced Rank Regression ; Model Selection

Abstract

In this paper we study the degrees of freedom of the reduced rank regression estimator in the framework of Stein's Unbiased Risk Estimation(SURE). We derive an unbiased estimator of the degrees of freedom of the reduced rank regression procedure. We show that it is significantly different than the number of free parameters in the model which is often taken as a heuristic estimate of be the degrees of freedom of an estimation procedure. With this one can easily employ various model-selection criteria such as Mallow's Cp or GCV to efficiently choose an optimal rank solution to the reduced rank regression problem which successfully avoids computationally expensive data-perturbation or bootstrap based methods. We demonstrate the advantages of this estimator through simulations as well as some applications to data examples and conclude with some extensions of this technique to other related estimation procedures.