Linear Smoothers and Additive Models

By Byandreas Buja, Trevor J. Hastie, Robert Tibshirani. 1989

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Citations in the corpus

Additive models with trend filtering (2017, methodology): “Buja et al. (1989) provide a unified analysis of additive models with linear smoothers, λQj = S + j − I, for j = 1, . . . , d, in which they describe the effective degrees of freedom of the resulting estimators and a generalized cross-validation routine for tuning; they also study fundamental proper”
Sparse additive models (2007, methodology): “Wasserman algorithm should also be investigated; convergence of special cases of standard backfitting was studied by Buja et al. (1989). An additional direction for future work is to develop procedures for automatic bandwidth selection in each dimension. We have used plug-in bandwidths and truncatio”
Nonparametric Inferences for Additive Models (2005, methodology): “In practice, the backfitting algorithm (Buja et al. 1989) is usually used to solve these equations, and the backfitting estimators converge to the solution   m̂1 m̂2 .”
Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models (2004, methodology): “imized (1) by modified backfitting (Buja et al., 1989), in which the component functions can be estimated using no more than simple linear scatterplot smoothers and standard least squares methods. However, θi estimation and reliable confidence interval calculation is difficult to integrate into this”
cutpointr: Improved Estimation and Validation of Optimal Cutpoints in R (2020, background): “Spline smoothing ﬁnds a cubic spline g that minimizes n 1 where the smoothing parameter λ is a ﬁxed tuning constant (Buja, Hastie, and Tibshirani 1989).”
Regularization Theory and Neural Networks Architectures (1995, background): “Additive models are well known in statistics (Hastie and Tibshirani 1986, 1987, 1990; Stone 1985; Wahba 1990; Buja et al. 1989) and can be considered as a generalization of linear models.”
FWDselect : Variable selection algorithm in regression models (2013, unknown): “To date, several approaches to estimating the model in (1) have been suggested in the statistical literature, e.g., Buja et al. (1989); Härdle and Hall (1993); Mammen et al. (1999).”
Local Likelihood Estimation in Generalized Additive Models (2003, background): “Early results on backfitting estimates in additive models with normal response are found in Buja et al. (1989).”
The VGAM Package for Categorical Data Analysis (2010, methodology): “VGAMs are estimated by applying a modiﬁed vector backﬁtting algorithm (cf. Buja et al. 1989) to the z i .”