Spline smoothing and nonparametric regression

By Brian S. Yandell. 1989

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Citations in the corpus

Deep learning in neural networks: An overview (2014, methodology): “Often weight priors are implicit in additional penalty terms (MacKay, 1992) or in methods based on validation sets (Craven & Wahba, 1979; Eubank, 1988; Golub, Heath, & Wahba, 1979; Hastie & Tibshirani, 1990; Mosteller & Tukey, 1968; Stone, 1974), Akaike’s information criterion and final prediction…”
Maximum likelihood estimation of a multi‐dimensional log‐concave density (2008, methodology): “, 1996), splines (Eubank, 1988; Wahba, 1990), penalized likelihood (Eggermont and LaRiccia, 2001) and vector support methods (Vapnik and Mukherjee, 2000).”
Weighted Nadaraya–Watson regression estimation (2001, background): “All rights reserved PII: S0167 -7152(00)00172 -3 refer to the books by Eubank (1988), M uller (1988), H ardle (1990), Wahba (1990), Hastie and Tibshirani (1990), Green and Silverman (1994), Wand and Jones (1995), Simono (1996), Fan and Gijbels (1996), Bosq (1998), among others.”
Adaptive Bayesian Regression Splines in Semiparametric Generalized Linear Models (2000, methodology): “For details and e cient algorithms for computing this basis see Eubank (1988) or Schumaker (1993), and especially for natural splines Lyche and Schumaker (1973) or Lyche and Str m (1996).”
On the Cox Model With Time-Varying Regression Coefficients (2005, unknown): “…− e(β, s) ] s(0){β0(s), s}λ0(s)ds. (A.4) Note that if ω(·) is a generic function with second derivatives bounded by a constant c, then, by a Taylor series expansion, it can be shown (Eubank 1988, p. 128) that ∥∥∥∥ ∫ h−1n K ( s − t hn ) {ω(s) − ω(t)}ds ∥∥∥∥ ≤ 1 2 ch2n, (A.5) where t ∈ [hn, τ − hn].”
Free‐knot polynomial splines with confidence intervals (2003, methodology): “Because of analytical and computational advantages the standard B-spline basis is used below, though its natural spline version could be used instead (Eubank, 1988; Greville, 1969).”
Smoothing splines estimators for functional linear regression (2009, background): “In order to verify existence of α̂, let us first cite some properties of the eigenvalues of pAm which have been studied by many authors (see Eubank [13]).”
Locally weighted polynomial regression: Parameter choice and application to forecasts of the Great Salt Lake (2006, methodology): “Some monographs that make this literature accessible are by Silverman [1986], Eubank [1988], and Härdle [1989]. Examples of nonparametric estimators include orthogonal series expansions, moving averages, splines, kernel, nearest neighbor, and neural network estimators. The reader is referred to Lall”
Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis (2014, methodology): “We assume that the overall mean function is estimated well enough (Kulasekera, 1995); this is the case when kernel or spline smoothing techniques (Eubank, 1988; © 2014 Board of the Foundation of the Scandinavian Journal of Statistics.”
Using Mutation Analysis for Assessing and Comparing Testing Coverage Criteria (2006, methodology): “26 available data as for the coverage criteria Am curves, except that a smoothing spline was used [9] to achieve better fit (R(2) = 0.”
A regularization approach to the many instruments problem (2012, background): “These three regularizations are taken from the literature on inverse problems, see Kress (1999) and Carrasco et al.”
A review on design, modeling and applications of computer experiments (2006, methodology): “For model assessment and selection, we refer the reader to Chapter 2 of Eubank (1988).”
Penalized regression with model‐based penalties (2000, methodology): “In practice, we usually have a general idea of the favoured functions uj, but we may need to estimate a parameter vector θ before these functions, properly denoted as uj(t; θ), can be completely specified.”
Flat Minima (1997, methodology): “Such assumptions are implicit in methods based on validation sets (Mosteller & Tukey, 1968; Stone, 1974; Eubank, 1988; Hastie & Tibshirani, 1993), e.g., \generalized cross validation" (Craven & Wahba, 1979; Golub et al., 1979), \\nal prediction error" (Akaike, 1970), \generalized prediction error"…”