Abstract
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.
Original language | English |
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Pages (from-to) | 77-93 |
Number of pages | 17 |
Journal | Journal of Statistical Planning and Inference |
Volume | 184 |
DOIs | |
Publication status | Published - 2017 May 1 |
Bibliographical note
Publisher Copyright:© 2017 Elsevier B.V.
Keywords
- Adaptive estimation
- Coordinate descent algorithm
- LASSO
- Oracle inequalities
- Penalized least squares
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics