Theory & Methods: Spatially‐adaptive Penalties for Spline Fitting

By David Ruppert, Raymond J. Carroll. 2000

284 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aa525f116384fedab7405d6eec13495460389f68

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Citations in the corpus

Inference for the Population Total from Probability-Proportional-to-Size Samples Based on Predictions from a Penalized Spline Nonparametric Model (2003, methodology): “In the spirit of Ruppert and Carroll (2000), Ruppert (2002) and others, we favor a modeling strategy that places a large number of knots (for example, 15 or 30) at pre-specified locations, and then achieves smoothness by treating mpp ++ ββ ,...,1 as random effects centered at 0.”
Spatially Adaptive Bayesian Penalized Regression Splines (P-splines) (2005, methodology): “Allowing the smoothing parameter to be spatially adaptive also helps improve the mean squared error (MSE) of the fits, as well as the accuracy of inference (Ruppert and Carroll 2000; Wand 2000).”
On algorithms for ordinary least squares regression spline fitting: A comparative study (2002, background): “Recent related references include Denison, Mallick and Smith (1998a), DiMatteo, Genovese and Kass (2001), Eilers and Marx (1996), Lindstrom (1999), Ruppert and Carroll (2000), Smith and Kohn (1996).”
Component selection and smoothing in smoothing spline analysis of variance models -- COSSO (2003, methodology): “A method that is commonly employed in the smoothing spline method to reduce computation load is the parsimonious bases approach used by Xiang and Wahba (1996), Ruppert and Carroll (2000), Lin, Wahba, Xiang, Gao, Klein and Klein (2000) and Yau, Kohn and Wood (2002). It has been shown that the number ”
Bayesian P-Splines (2004, methodology): “Such situations have attained considerable attention in the recent literature; see, for example, Luo and Wahba (1997) and Ruppert and Carroll (2000).”
Model-assisted estimation for complex surveys using penalised splines (2005, background): “Eilers and Marx (1996) introduced penalized spline smoothers (often called P-splines), and further developments and results on these low-rank smoothers have been obtained by Ruppert and Carroll (2000) and Wand (2003).”
Determination of linear components in additive models (2011, methodology): “The penalised spline method for nonparametric regression was first proposed by Wahba (1990), and deeply studied by Eilers and Marx (1996) and Ruppert and Carroll (2000).”
Exact likelihood ratio tests for penalised splines (2005, methodology): “I Penalised-spline additive models described in Marx & Eilers (1998), Ruppert & Carroll (2000) and Aerts et al. (2002) have the advantage that they require only a small set of spline basis functions for each covariate and can be represented as mixed models (Brumback et al., 1999).”
Some theory for penalized spline generalized additive models (2002, background): “Ruppert and Carroll (2000) describe an algorithm for choosing the number of knots, and demonstrate its eectiv eness through simulation.”
Smoothing and forecasting mortality rates (2004, background): “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).”
Bayesian Smoothing and Regression Splines for Measurement Error Problems (2002, methodology): “Their methods are based on xed-knot regression splines (or polynomial splines; see Eilers and Marx 1996; Ruppert and Carroll 2000; Sec.”
Estimating the Interest Rate Term Structure of Corporate Debt With a Semiparametric Penalized Spline Model (2004, background): “Once the number of knots is selected, the knots are located at equally spaced points as in Eilers and Marx (1996) or, as in Ruppert and Carroll (2000) and in Section 7, at equally spaced quantiles of the independent variable.”
Marginal Longitudinal Nonparametric Regression (2002, methodology): “The purpose of this article is to investigate whether the kernel result holds for marginal spline methods, especially smoothing splines (see Wahba 1990; Green and Silverman 1994 among many others) and penalized regression splines (P-splines) (see Eilers and Marx 1996; Ruppert and Carroll 2000).”
Smoothing and mixed models (2003, background): “More recent references are Eilers and Marx (1996), Hastie (1996) and Ruppert and Carroll (2000) where the following names:”
Centre for Efficiency and Productivity Analysis (2003, background): “(1999), Fahrmeier (2000), Koop & Poirier (2001), Ruppert & Carroll (2000) and Berry”
A COMPARISON OF MIXED MODEL SPLINES FOR CURVE FITTING (2007, methodology): “Penalized splines based on a truncated power function (TPF) basis were introduced by Brumback et al. (1999) and Ruppert & Carroll (2000), and a full exposition in the mixed model setting was given by Wand (2003) and Ruppert et al. (2003).”