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 |
|---|---|
| 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 |
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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
Cite this
Penalized B-spline estimator for regression functions using total variation penalty. / Jhong, Jae Hwan; Koo, Ja Yong; Lee, Seong Whan.
In: Journal of Statistical Planning and Inference, Vol. 184, 01.05.2017, p. 77-93.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Penalized B-spline estimator for regression functions using total variation penalty
AU - Jhong, Jae Hwan
AU - Koo, Ja Yong
AU - Lee, Seong Whan
PY - 2017/5/1
Y1 - 2017/5/1
N2 - 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.
AB - 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.
KW - Adaptive estimation
KW - Coordinate descent algorithm
KW - LASSO
KW - Oracle inequalities
KW - Penalized least squares
UR - http://www.scopus.com/inward/record.url?scp=85008598998&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85008598998&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2016.12.003
DO - 10.1016/j.jspi.2016.12.003
M3 - Article
AN - SCOPUS:85008598998
VL - 184
SP - 77
EP - 93
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
ER -