On the degrees of freedom in shrinkage estimation

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 differen...

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Bibliographic Details
Published inJournal of multivariate analysis Vol. 100; no. 7; pp. 1338 - 1352
Main Author Kato, Kengo
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.08.2009
Elsevier
Taylor & Francis LLC
SeriesJournal of Multivariate Analysis
Subjects
AIC
AIC Degrees of freedom Fused Lasso Group Lasso Lasso Mallows' Cp Second fundamental form Shrinkage estimation Stein's lemma Tubal coordinates
Convex and discrete geometry
Degrees of freedom
Estimating techniques
Exact sciences and technology
Fused Lasso
Geometry
Group Lasso
Lasso
Linear inference, regression
Mallows’ [formula omitted]
Mathematics
Multivariate analysis
Parameter estimation
Probability and statistics
Regression analysis
Sciences and techniques of general use
Second fundamental form
Shrinkage estimation
Statistics
Stein’s lemma
Studies
Tubal coordinates
Group Lasso
Degrees of freedom
62J05
Mallows’ C p
62J07
Stein’s lemma
Lasso
Second fundamental form
Fused Lasso
Tubal coordinates
AIC
Shrinkage estimation
Ridge regression
Freedom degree
Convex set
Shrinkage estimator
Statistical estimation
Multivariate analysis
Stein's lemma
Statistical method
Statistical regression
Regression coefficient
Unbiased estimation
Mallows' Cp
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Summary: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 C p type criterion and AIC for selecting tuning parameters.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2008.12.002