Nonparametric regression and generalized linear models

By Peter J. Green, Bernard Walter Silverman. 1994

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Citations in the corpus

High-dimensional additive modeling (2008, methodology): “2 in [13] we can construct natural cubic splines ĝj with knots at x (j) i , i = 1, .”
Adaptive piecewise polynomial estimation via trend filtering (2013, methodology): “Smoothing splines are a popular tool in nonparametric regression, and have been extensively studied in terms of both computations and theory [some well-known references are de Boor (1978), Wahba (1990), Green and Silverman (1994)].”
SPLINE ESTIMATORS FOR THE FUNCTIONAL LINEAR MODEL (2003, methodology): “We consider a generalized cross validation criterion for the choice of K and ρ because it is computationally fast, widely used as an automatic procedure to choose a smoothing parameter, and has been proved to be efficient in many statistical settings (Green and Silverman (1994)).”
Spatial modelling using a new class of nonstationary covariance functions (2006, methodology): “The third method (tps) fits the surface as a thin plate spline (Green and Silverman 1994), using the Tps() function in the fields library in R, in which the smoothing parameter is chosen automatically by generalized cross-validation (GCV).”
On algorithms for ordinary least squares regression spline fitting: A comparative study (2002, background): “Other basis functions for regression spline fitting also exist, such as those for B-splines, natural splines and radial basis functions (e.g., see Eilers and Marx, 1996; Green and Silverman, 1994).”
Thin plate regression splines (2003, background): “See Wahba (1990) or Green and Silverman (1994) for further information about thin plate splines.”
Smoothing: Local Regression Techniques (2012, background): “Books devoted to spline smoothing include Green and Silverman (1994) and Wahba (1990).”
Functional linear discriminant analysis for irregularly sampled curves (2001, methodology): “We choose to use natural cubic spline functions because of their desirable mathematical properties and easy implementation (de Boor (1978), Green and Silverman (1994)).”
Generalized linear models with functional predictors (2002, methodology): “We choose to make use of natural cubic splines (Silverman, 1985; Green and Silverman, 1994).”
Spatial‐Process Estimates as Smoothers (2012, background): “…regression and smoothing, the assumptions on h are based on higher order derivatives and in the case of thin plate splines (Wahba 1990a, Green and Silverman 1994) the degree of P and the dimension of x imply a speciic roughness penalty on h based on integrated squared (partial)…”
GAMs with integrated model selection using penalized regression splines and applications to environmental modelling (2002, methodology): “One standard method for avoiding knot placement problems is to use smoothing splines or penalized regression splines (both options are discussed, for example, in Wahba, 1990 or Green and Silverman, 1994).”
One‐Way anova for Functional Data via Globalizing the Pointwise F‐test (2014, methodology): “…one to reconstruct fij .t/ via one of the existing smoothing techniques such as regression splines (Eubank, 1999), smoothing splines (Wahba, 1990; Green & Silverman, 1994), P -splines (Ruppert et al., 2003), local polynomial smoothing (Wand & Jones, 1995; Fan & Gijbels, 1996), and reproducing…”
Heat Effects on Mortality in 15 European Cities (2008, methodology): “First, we used a flexible parametric approach to describe the exposure-response curve, including in the model a cubic regression spline for apparent temperature with 1 knot every 8°C.(22) Second, to summarize and to address heterogeneity, we further described the relationship between apparent temper”
Stochastic Claims Reserving in General Insurance (2002, methodology): “For other distributions, such as the Poisson, the fitting procedure is extended using an iterative process, and has some similarity with the procedure used for fitting GLMs (see Hastie & Tibshirani, 1990; Green & Silverman, 1994).”