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On Generalized Cross-Validation for Multivariate Smoothing Spline Functions
SIAM Journal on Scientific and Statistical Computing, 1987The aim of this paper is to contribute to the study of generalized cross- validation showing that it satisfied an asymptotic optimality condition and to prove that under the assumption that the knots have an asymptotic behavior defined by a cumulative distribution function with bounded density. To prove the main theorem (Th.
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Generalized Cross Validation stopping rule for Iterated Tikhonov regularization
2021 21st International Conference on Computational Science and Its Applications (ICCSA), 2021Ill-posed inverse problems arise in many fields of science and engineering. These problems are usually very sensitive to the presence of noise in the measured data. Regularization methods aim at reducing this sensitivity. Among these methods Iterated Tikhonov (IT), in both its standard and general form, has been widely investigated due to its ease of ...
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Journal of Computational and Graphical Statistics, 2004
This article presents a modified Newton method for minimizing multidimensional bandwidth selection for estimation in generalized additive models. The method is based on the generalized cross-validation criterion applied to backfitting estimates. The approach in particular is applicable to higher dimensional problems and provides a computationally ...
Kauermann, Göran, Opsomer, JD
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This article presents a modified Newton method for minimizing multidimensional bandwidth selection for estimation in generalized additive models. The method is based on the generalized cross-validation criterion applied to backfitting estimates. The approach in particular is applicable to higher dimensional problems and provides a computationally ...
Kauermann, Göran, Opsomer, JD
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Smoothing Inversion of Fourier Series Using Generalized Cross-Validation
Results in Mathematics, 1996Let \(f\) be a 1-periodic, absolutely continuous function with \(\int_I |f'(t)|^2 dt< \infty\), where \(I=\) \([-1/2, 1/2]\). Instead of the exact Fourier coefficients of \(f\), \(\widehat f_k:= \int_I f(t) e^{- 2\pi ikt} dt\), only a finite sequence of noisy values of \(\widehat f_k\), \(\widehat y_k= \widehat f_k+ \widehat\varepsilon_k\) \((k= 0 ...
Tasche, Manfred, Weyrich, Norman
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Fast generalized cross validation using Krylov subspace methods
Numerical Algorithms, 2008The key step of the generalized cross-validation (GCV) method, used in a smoothing spline fitting of noisy data, is the computation of the optimal parameter \(\lambda \) by minimization of the GCV function \[ \text{GCV}(\lambda )= n\, {z^T (Q+\lambda I)^{-2} z \over [ \text{tr}\, ((Q+\lambda I)^{-1})]^2}, \] for the influence matrix \(Q\) and the ...
Roger B. Sidje +2 more
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Surface approximation by spline smoothing and generalized cross-validation
Mathematics and Computers in Simulation, 1992Abstract A technique is developed to approximate multi-dimensional surfaces based on smoothing splines. The tensor product is used to extend a one-dimensional spline basis to higher dimensions. The method of generalized cross-validation is applied to choose the smoothing parameter which is computed with the aid of the generalized singular value ...
Hongmin Lu, Frank H. Mathis
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Generalized cross‐validation as a stopping rule for the Richardson‐Lucy algorithm
International Journal of Imaging Systems and Technology, 1995AbstractThe Richardson‐Lucy (R‐L) algorithm has been widely used to restore degraded astronomical images. This algorithm is nothing more than the expectation‐maximization (EM) algorithm applied to Poisson data. The R‐L method is iterative in nature and converges to a (possibly local) maximum of the likelihood function. Unfortunately, because of the ill‐
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Smoothing Noisy Data Using Dynamic Programming and Generalized Cross-Validation
Journal of Biomechanical Engineering, 1988Smoothing and differentiation of noisy data using spline functions requires the selection of an unknown smoothing parameter. The method of generalized cross-validation provides an excellent estimate of the smoothing parameter from the data itself even when the amount of noise associated with the data is unknown.
C R, Dohrmann, H R, Busby, D M, Trujillo
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Generalized least squares cross‐validation in kernel density estimation
Statistica Neerlandica, 2015The kernel density estimation is a popular method in density estimation. The main issue is bandwidth selection, which is a well‐known topic and is still frustrating statisticians. A robust least squares cross‐validation bandwidth is proposed, which significantly improves the classical least squares cross‐validation bandwidth for its variability and ...
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Gcvpack – routines for generalized cross validation
Communications in Statistics - Simulation and Computation, 1987Douglas M. Bates +3 more
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