On the asymptotics of penalized spline smoothing

By Xiao Wang, Jinglai Shen, David Ruppert. 2011

57 citations recorded by the source corpus.

Abstract: This paper performs an asymptotic analysis of penalized spline estimators. We compare P -splines and splines with a penalty of the type used with smoothing splines. The asymptotic rates of the supremum norm of the difference between these two estimators over compact subsets of the interior and over the entire interval are established. It is shown that a Pspline and a smoothing spline are asymptotically equivalent provided that the number of knots of the P-spline is large enough, and the two estimators have the same equivalent kernels for both interior points and boundary points.

Subfields: Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/38dc53429287ad96efe736e0dc57960b931b4a4e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Statistics and Probability

Citations in the corpus

Fast bivariate P‐splines: the sandwich smoother (2010, methodology): “We shall use the equivalent kernel method that was first used for studying smoothing splines (Silverman, 1984) and also useful in studying the asymptotics of P-splines (Li and Ruppert, 2008; Wang et al., 2011).”
Smoothing Parameter and Model Selection for General Smooth Models (2015, background): “plines There is already a detailed literature on the asymptotic properties of penalized regression splines (e.g. Gu and Kim, 2002;Hall and Opsomer, 2005;Kauermann et al., 2009;Claeskens et al., 2009; Wang et al., 2011;Yoshida and Naito, 2014). Rather than reproduce that literature, the purpose of th”
Twenty years of P-splines (2015, unknown): “See Li and Ruppert (2008); Claeskens et al. (2009); Kauermann et al. (2009); Wang et al. (2011).”