Some asymptotic results on generalized penalized spline smoothing

By Goeran Kauermann, Tatyana Krivobokova, Ludwig Fahrmeir. 2009

163 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/584708d950a33550cbbc0ee05aace23ef3d57353

How researchers see this paper

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

In Artificial Intelligence

1. Simon N. Wood
2. Andrea Riebler
3. Daniel P. Simpson
4. Finn Lindgren
5. Håvard Rue
6. Sigrunn Holbek Sørbye
7. Goeran Kauermann
8. J. Illian

In Environmental Engineering

1. Daniel P. Simpson
2. Håvard Rue
3. Finn Lindgren
4. Andrea Riebler
5. Sigrunn Holbek Sørbye
6. Thomas Kneib
7. Simon N. Wood
8. J. Illian

In Statistics and Probability

1. Simon N. Wood
2. Thomas Kneib
3. Daniel P. Simpson
4. Andrea Riebler
5. Finn Lindgren
6. Håvard Rue
7. Goeran Kauermann
8. Stefan Lang

Citations in the corpus

• Fast bivariate P‐splines: the sandwich smoother (2010, background): “An asymptotic study of univariate penalized splines was achieved only recently (Opsomer and Hall, 2005; Li and Ruppert, 2008; Claeskens et al. , 2009; Kauermann et al. , 2009; Wang et al. , 2011).”
• Shape constrained additive models (2015, background): “Asymptotic properties of P-splines were also studied in Kauermann et al. (2009) and Claeskens et al. (2009).”
• Twenty years of P-splines (2015, unknown): “See Li and Ruppert (2008); Claeskens et al. (2009); Kauermann et al. (2009); Wang et al. (2011).”
• Simultaneous Confidence Bands for Penalized Spline Estimators (2010, background): “Some first results were presented by Hall and Opsomer (2005), Li and Ruppert (2008), and Kauermann, Krivobokova, and Fahrmeir (2009).”
• Bayesian Computing with INLA: A Review (2016, background): “Theoretical results for the current rather “vague” context are difficult to obtain and constitute a largely unsolved problem; see for example Shun and McCullagh (1995); Kauermann et al. (2009); Ogden (2016).”
• 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).”
• Fast Calibrated Additive Quantile Regression (2017, methodology): “This includes the regime considered by Kauermann, Krivobokova, and Fahrmeir (2009), when demonstrating the statistical validity of GAM inference based on Laplace approximate marginal likelihood smoothing parameter estimation.”
• Flexible Copula Density Estimation with Penalized Hierarchical B‐splines (2013, methodology): “D/; D 0, we obtain with simple regular expansion techniques (see, e.g. Kauermann et al. (2009)) OQb.”
• Smoothing Parameter and Model Selection for General Smooth Models (2015, background): “kman, 1985), which Hall and Opsomer (2005) show also applies to penalized cubic regression splines as considered here. This rate suggests using k = O(nα), α ≥ 1/5. However, in quite general settings, Kauermann et al. (2009) demonstrate the theoretical well-foundedness of penalized regression splines”