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


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.


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Luo Xiao. "Asymptotic theory of penalized splines." Electron. J. Statist. 13 (1) 747 - 794, 2019.


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

Primary: 62G08, 62G20


Vol.13 • No. 1 • 2019
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