文章基本信息

标题：Asymptotic theory of penalized splines
本地全文：下载
作者：Luo Xiao
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：1
页码：747-794
DOI：10.1214/19-EJS1541
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.