Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1146969 | Journal of Multivariate Analysis | 2009 | 15 Pages |
Abstract
We study the degrees of freedom in shrinkage estimation of regression coefficients. Generalizing the idea of the Lasso, we consider the problem of estimating the coefficients by minimizing the sum of squares with the constraint that the coefficients belong to a closed convex set. Based on a differential geometric approach, we derive an unbiased estimator of the degrees of freedom for this estimation method, under a smoothness assumption on the boundary of the closed convex set. The result presented in this paper is applicable to estimation with a wide class of constraints. As an application, we obtain a CpCp type criterion and AIC for selecting tuning parameters.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
Kengo Kato,