Translator Disclaimer
2019 Asymptotic theory of penalized splines
Luo Xiao
Electron. J. Statist. 13(1): 747-794 (2019). DOI: 10.1214/19-EJS1541

Abstract

The paper gives a unified study of the large sample asymptotic theory of penalized splines including the O-splines using B-splines and an integrated squared derivative penalty [22], the P-splines which use B-splines and a discrete difference penalty [13], and the T-splines which use truncated polynomials and a ridge penalty [24]. Extending existing results for O-splines [7], it is shown that, depending on the number of knots and appropriate smoothing parameters, the $L_{2}$ risk bounds of penalized spline estimators are rate-wise similar to either those of regression splines or to those of smoothing splines and could each attain the optimal minimax rate of convergence [32]. In addition, convergence rate of the $L_{\infty }$ risk bound, and local asymptotic bias and variance are derived for all three types of penalized splines.

Citation

Download Citation

Luo Xiao. "Asymptotic theory of penalized splines." Electron. J. Statist. 13 (1) 747 - 794, 2019. https://doi.org/10.1214/19-EJS1541

Information

Received: 1 September 2018; Published: 2019
First available in Project Euclid: 21 March 2019

zbMATH: 07056140
MathSciNet: MR3925516
Digital Object Identifier: 10.1214/19-EJS1541

Subjects:
Primary: 62G08, 62G20

JOURNAL ARTICLE
48 PAGES


SHARE
Vol.13 • No. 1 • 2019
Back to Top