Some theory for penalized spline generalized additive models

By Marc Aerts, Gerda Claeskens, Matt P. Wand. 2002

64 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d145c7c187314c00e1331452f33727d9f93e54c3

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In Applied Mathematics

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Citations in the corpus

Theory for penalised spline regression (2005, methodology): “When penalties are used in combination with a fixed basis, Wand (1999) derived an asymptotic approximation of P-splines mean squared error, and Aerts et al. (2002) extended this result to the generalised and multivariate regression contexts.”
Restricted likelihood ratio lack‐of‐fit tests using mixed spline models (2004, methodology): “The estimator can also be formulated in terms of other bases such as the Demmler–Reinsch basis (Nychka and Cummins, 1996) and the B-spline basis (Eilers and Marx, 1996).”
Flexible smoothing with P-splines: a unified approach (2002, methodology): “(2001) and Aerts et al. (2002) applied the mixed model approach to generalized additive models.”
Smoothing and forecasting mortality rates (2004, methodology): “Theoretical aspects of P-splines are discussed in Wand (1999), Ruppert and Carroll (2000), Aerts et al. (2002), Ruppert (2002) and Durban and Currie (2003).”
Model-assisted estimation for complex surveys using penalised splines (2005, unknown): “Incorporating multiple covariates as well as combinations of categorical variables, para metric and nonparametric terms, is straightforward, as shown in Aerts et al. (2002).”
Determination of linear components in additive models (2011, methodology): “…been investigated lately, such as the single-index component estimation in additive models in Yu and Ruppert (2002), generalised additive models in Aerts, Claeskens, and Wand (2002), small area estimation in Opsomer, Claeskens, Ranalli, Kauermann, and Breidt (2008), and Spline-backfitted kernel…”
Local Likelihood Estimation in Generalized Additive Models (2003, methodology): “Recently, Aerts et al. (2002) discussed penalized regression spline estimators for additive and generalized additive models, and propose Fisher scoring as the fitting method.”
Some asymptotic results on generalized penalized spline smoothing (2009, unknown): “Some first results were provided in Wand (1999) and Aerts et al. (2002), who used the simplifying assumption that the dimension of the spline basis is fixed.”