Penalized B-spline estimator for regression functions using total variation penalty

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• 作者：Jae-Hwan Jhong^a ; Ja-Yong Koo^a ; ^{jykoo@korea.ac.kr} ; Seong-Whan Lee^b
• 关键词：Adaptive estimation ; Coordinate descent algorithm ; LASSO ; Oracle inequalities ; Penalized least squares
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：184
• 期：Complete
• 页码：77-93
• 全文大小：714 K
• 卷排序：184

文摘

We carry out a study on a penalized regression spline estimator with total variation penalty. In order to provide a spatially adaptive method, we consider total variation penalty for the estimating regression function. This paper adopts B-splines for both numerical implementation and asymptotic analysis because they have small supports, so the information matrices are sparse and banded. Once we express the estimator with a linear combination of B-splines, the coefficients are estimated by minimizing a penalized residual sum of squares. A new coordinate descent algorithm is introduced to handle total variation penalty determined by the B-spline coefficients. For large-sample inference, a nonasymptotic oracle inequality for penalized B-spline estimators is obtained. The oracle inequality is then used to show that the estimator is an optimal adaptive for the estimation of the regression function up to a logarithm factor.