On the asymptotics of penalized splines

By Yingxing Li, David Ruppert. 2008

184 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e21bf748873d451b236e89fe7d9908a7c46f19f8

How researchers see this paper

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

In Applied Mathematics

1. Li Wang
2. Ming-Jun Lai
3. Natalya Pya
4. Hua Liang
5. David Ruppert
6. Luo Xiao
7. Yingxing Li
8. Goeran Kauermann

In Statistics and Probability

1. Simon N. Wood
2. Thomas Kneib
3. Hua Liang
4. Stefan Lang
5. David Ruppert
6. Natalya Pya
7. Li Wang
8. Goeran Kauermann

Citations in the corpus

• Variational inference for count response semiparametric regression (2013, unknown): “Theoretical underpinning for this last aspect is given in Li and Ruppert (2008).”
• Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling (2014, methodology): “In this article, we adopt the penalized splines (Ruppert, Wand, and Carroll 2003; Li and Ruppert 2008; Claeskens, Krivobokova, and Opsomer 2009; Wu, Xue, and Kumar 2012) to obtain the estimates, ˆ X k ( t ) and ˆ X k ( t ), k = 1 , . . . , p .”
• Penalized Functional Regression (2011, unknown): “In the smoothing literature, the choice of the number of knots in φ has been shown (Ruppert 2002; Li and Ruppert 2008) to be unimportant as long as it is large enough to capture the maximum complexity of the regression function: in penalized spline regression it is the explicit smoothness…”
• Well-Being over the Life Span: Semiparametric Evidence from British and German Longitudinal Data (2009, methodology): “In addition, P-spline regression is an established method whose asymptotic behavior is well known and normal (Yu & Ruppert, 2002; Li & Ruppert, 2008; Kauermann et al., 2009).”
• Some asymptotic results on generalized penalized spline smoothing (2009, background): “mal response models but differ from of Li & Ruppert (2006) .”
• A Note on Penalized Spline Smoothing With Correlated Errors (2007, background): “Some first results have been given by Cardot (2002), Hall and Opsomer (2005), and Li and Ruppert (2007).”
• On the asymptotics of penalized spline smoothing (2011, methodology): “Li and Ruppert [13], our approach considerably simplifies the development and yields an instrumental alternative to establish the equivalent kernels for general penalized splines.”
• Density Estimation in the Presence of Heteroscedastic Measurement Error (2008, background): “The asymptotic theory of penalized B-splines with an increasing number of knots was developed recently by Li and Ruppert (2007) for nonparametric regression without measurement error.”
• Simultaneous Confidence Bands for Penalized Spline Estimators (2010, background): “can be found in Hall and Opsomer (2005), Li and Ruppert (2008) and Kauermann et al.”
• Nonparametric M-quantile regression using penalised splines (2009, background): “The asymptotic properties of classical p-spline estimators when the number of knots is allowed to grow have been studied only very recently in [29].”
• Shape constrained additive models (2015, background): “As with any penalized regression spline approaches, the choice of the basis dimension, q, is not crucial but should be generous enough to avoid oversmoothing/underfitting (Ruppert 2002; Li and Ruppert 2008).”
• The Hodrick-Prescott Filter A Special Case of Penalized Spline Smoothing (2010, methodology): “The choice of degree of polynomial (p) and number of knots (K) is not so crucial (Ruppert et al., 2003), since the asymptotic distribution of a penalized spline does not depend on p or K, provided the latter increases sufficiently rapidly (Li and Ruppert, 2008, Wang, Shen, and Ruppert, 2010).”
• Bivariate Penalized Splines for Regression (2013, methodology): “Compared with (A4), (A4’) further requires that the number of triangles be above some minimum depending upon the degree of the spline, which is similar to the requirement of Li and Ruppert (2008) in the univariate case.”
• Fast bivariate P‐splines: the sandwich smoother (2010, methodology): “Let P E-M denote the penalty matrix for the E-M estimator, then The first and second penalty terms in bivariate P-splines penalize the columns and rows of Θ , respectively, and are thus called column and row penalties.”
• Twenty years of P-splines (2015, unknown): “See Li and Ruppert (2008); Claeskens et al. (2009); Kauermann et al. (2009); Wang et al. (2011).”
• Determination of linear components in additive models (2011, methodology): “marginal integration (Linton and Nielsen 1995). Barry (1993), Chen, Liu, and Tsay (1995), Härdle and Tsybakov (1995), Sperlich, Tjøstheim, and Yang (2002), and Härdle, Huet, Mammen, and Sperlich (2004) have proposed methods to test for additivity, and thereby obtain diagnostic fools for using additi”