Some Aspects of the Spline Smoothing Approach to Non‐Parametric Regression Curve Fitting

By Bernard Walter Silverman. 1985

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Citations in the corpus

GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learning (2021, methodology): “A common approach to handle large datasets is to learn a small set of inducing points, which act as a proxy for the training data (Silverman, 1985; Quinonero-Candela & Rasmussen, 2005; Snelson & Ghahramani, 2006).”
Stochastic Variational Deep Kernel Learning (2016, background): “Many promising approaches to scalability have been explored, for example, involving randomized methods [21, 17, 32] , and low rank approximations [24, 20].”
Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP) (2015, methodology): “Hensman et al., 2013; Quiñonero-Candela & Rasmussen, 2005; Silverman, 1985) have been introduced to scale up GPs to larger datasizes.”
Generalized Additive Models for Exceedances of High Thresholds With an Application to Return Level Estimation for U.S. Wind Gusts (2019, methodology): “Inference for β can be performed by maximizing a penalized likelihood (Silverman 1985) of the form p(y; β , λ) = log f (y; β) − 12β ′Sλβ , where Sλ is a penalty matrix that depends on smoothing parameters λ = (λ1, . . . , λK), which control the smoothness of g.”
Thin plate regression splines (2003, methodology): “See Wahba (1990) or Green and Silverman (1994) for further information about thin plate splines.”
Regularization of Wavelet Approximations (2001, methodology): “It was discussed by Silverman (1985) and consists of 133 observations from a crash test and shows the acceleration of a motorcyclist’s head during a crash.”
Generalized Additive Models (2006, unknown): “Following Wahba (1983) and Silverman (1985), we can recognize that, by imposing a particular penalty, we are effectively imposing some prior beliefs about the likely characteristics of the correct model.”
GAMs with integrated model selection using penalized regression splines and applications to environmental modelling (2002, background): “…at convergence: z|β ∼ N(Xβ, Iσ2) and by assuming a multivariate normal prior on β with mean 0 and covariance matrix proportional to an appropriate pseudoinverse of ∑ k λkHk: see Hastie and Tibshirani, (1990) section 3.6, based on Silverman (1985) (they assume square X, but this is not necessary).”
Signal extraction and the formulation of unobserved components models (2000, methodology): “(cid:13) Silverman (1985) estimates by cross-validation, but does not report its value.”
Models of the Aging Brain Structure and Individual Decline (2012, unknown): “The idea of spline regression is to determine an “optimal” age trajectory that maximizes its goodness of fit and the smoothness at the same time (Craven and Wahba, 1978; Silverman, 1985; Wahba, 1990).”
Sieve Empirical Likelihood and Extensions of the Generalized Least Squares (2003, background): “Especially, R̂M ðhÞ recovers the objective function for weighting the unequal variances of errors suggested by Silverman (1985) in his smoothing spline estimator.”