REGRESSION ON MANIFOLDS: ESTIMATION OF THE EXTERIOR DERIVATIVE

• 成果类型: Article
• 署名作者: Aswani, Anil; Bickel, Peter; Tomlin, Claire
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS823
• 发表日期: 2011
• 页码: 48-81
• 关键词: period-cohort analysis; Nonparametric Regression; variable selection; Lasso; MODEL; regularization; components; asymptotics

摘要

Collinearity and near-collinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the regression coefficients, and interpretation of the coefficients is ambiguous because gradients are not defined. Using a differential geometric interpretation, in which the regression coefficients are interpreted as estimates of the exterior derivative of a function, we develop a new method to do regression in the presence of collinearities. Our regularization scheme can improve estimation error, and it can be easily modified to include lasso-type regularization. These estimators also have simple extensions to the large p, small n context.