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

Jae Hwan Jhong, Ja Yong Koo, Seong Whan Lee

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)77-93
Number of pages17
JournalJournal of Statistical Planning and Inference
Volume184
DOIs
Publication statusPublished - 2017 May 1

Fingerprint

Regression Function
Total Variation
B-spline
Splines
Penalty
Oracle Inequalities
Estimator
Penalized Regression
Coordinate Descent
Regression Splines
Penalized Splines
Estimating Function
Information Matrix
Descent Algorithm
Adaptive Method
Sum of squares
Coefficient
Logarithm
Asymptotic Analysis
Asymptotic analysis

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 journalArticle

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