On Generalized Cross-Validation for Multivariate Smoothing Spline Functions

1987 ◽  
Vol 8 (4) ◽  
pp. 630-643 ◽  
Author(s):  
Florencio I. Utreras
Keyword(s):  
Cross Validation ◽  
Smoothing Spline ◽  
Spline Functions ◽  
Generalized Cross Validation ◽  
Multivariate Smoothing

Smoothing Noisy Data Using Dynamic Programming and Generalized Cross-Validation

1988 ◽  
Vol 110 (1) ◽  
pp. 37-41 ◽  
Author(s):  
C. R. Dohrmann ◽  
H. R. Busby ◽  
D. M. Trujillo
Keyword(s):  
Dynamic Programming ◽  
Cross Validation ◽  
Present Model ◽  
Noisy Data ◽  
Smoothing Parameter ◽  
Spline Functions ◽  
General Context ◽  
Simple Extension ◽  
Generalized Cross Validation ◽  
Selection Of

Smoothing 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. In the present model only a single smoothing parameter must be obtained, but in a more general context the number may be larger. In an earlier work, smoothing of the data was accomplished by solving a minimization problem using the technique of dynamic programming. This paper shows how the computations required by generalized cross-validation can be performed as a simple extension of the dynamic programming formulas. The results of numerical experiments are also included.

scholarly journals Goodness of Fit Test of an Autocorrelated Time Series Cubic Smoothing Spline Model

2021 ◽  
pp. 191-200
Author(s):  
Samuel Olorunfemi Adams ◽  
Davies Abiodun Obaromi ◽  
Alumbugu Auta Irinews
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Cross Validation ◽  
Real Life ◽  
Smoothing Spline ◽  
Selection Methods ◽  
Sample Sizes ◽  
Goodness Of Fit Test ◽  
Generalized Cross Validation ◽  
Non Parametric

We investigated the finite properties as well as the goodness of fit test for the cubic smoothing spline selection methods like the Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV) and Mallow CP criterion (MCP) estimators for time-series observation when there is the presence of Autocorrelation in the error term of the model. The Monte-Carlo study considered 1,000 replication with six sample sizes: 30; 60; 120; 240; 480 and 960, four degree of autocorrelations; 0.1; 0.3; 0.5; and 0.9 and three smoothing parameters; lambdaGML= 0.07271685, lambdaGCV= 0.005146929, lambdaMCP= 0.7095105. The cubic smoothing spline selection methods were also applied to a real-life dataset. The Predictive mean square error, R-square, and adjusted R-square criteria for assessing finite properties and goodness of fit among competing models discovered that the performance of the estimators is affected by changes in the sample sizes and autocorrelation levels of the simulated and real-life data set. The study concluded that the Generalized Cross-Validation estimator provides a better fit for Autocorrelated time series observation. It is recommended that the GCV works well at the four autocorrelation levels and provides the best fit for time-series observations at all sample sizes considered. This study can be applied to; non –parametric regression, non –parametric forecasting, spatial, survival and econometric observations.

scholarly journals Penerapan Generalized Cross Validation dalam Model Regresi Smoothing Spline pada Produksi Ubi Jalar di Jawa Tengah

2019 ◽  
Vol 1 (2) ◽  
pp. 117
Author(s):  
Trionika Dian Wahyuningsih ◽  
Sri Sulistijowati Handajani ◽  
Diari Indriati
Keyword(s):  
Sweet Potato ◽  
Nonparametric Regression ◽  
Cross Validation ◽  
Animal Feed ◽  
Organic Fertilizer ◽  
Specific Pattern ◽  
Production Model ◽  
Smoothing Spline ◽  
Urea Fertilizer ◽  
Generalized Cross Validation

<p>Sweet Potato is a useful plant as a source carbohydrates, proteins, and is used as an animal feed and ingredient industry. Based on data from the Badan Pusat Statistik (BPS), the production fluctuations of the sweet potato in Central Java from year to year are caused by many factor. The production of sweet potato and the factors that affected it if they are described into a pattern of relationships then they do not have a specific pattern and do not follow a particular distribution, such as harvest area, the allocation of subsidized urea fertilizer, and the allocation of subsidized organic fertilizer. Therefore, the production model of sweet potato could be applied into nonparametric regression model. The approach used for nonparametric regression in this study is smoothing spline regression. The method used in regression smoothing spline is generalized cross validation (GCV). The value of the smoothing parameter (λ) is chosen from the minimum GCV value. The results of the study show that the optimum λ value for the factors of harvest area, urea fertilizer and organic fertilizer are 5.57905e-14, 2.51426e-06, and 3.227217e-13 that they result a minimum GCV i.e 2.29272e-21, 1.38391e-16, and 3.46813e-24.</p><p> </p><p><strong>Keywords</strong>: Sweet potato; nonparametric; smoothing spline; generalized cross validation.</p>

A note on generalized cross-validation with replicates

1992 ◽  
Vol 14 (4) ◽  
pp. 283-287 ◽  
Author(s):  
Chong Gu ◽  
Nancy Heckman ◽  
Grace Wahba
Keyword(s):  
Cross Validation ◽  
Generalized Cross Validation

Automatic blind deconvolution with Toeplitz-structured sparse total least squares

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. V345-V357 ◽  
Author(s):  
Nasser Kazemi
Keyword(s):  
Least Squares ◽  
Cross Validation ◽  
Blind Deconvolution ◽  
Real Data ◽  
Total Least Squares ◽  
Data Matrix ◽  
Seismic Survey ◽  
Structural Constraints ◽  
Generalized Cross Validation ◽  
Free Data

Given the noise-corrupted seismic recordings, blind deconvolution simultaneously solves for the reflectivity series and the wavelet. Blind deconvolution can be formulated as a fully perturbed linear regression model and solved by the total least-squares (TLS) algorithm. However, this algorithm performs poorly when the data matrix is a structured matrix and ill-conditioned. In blind deconvolution, the data matrix has a Toeplitz structure and is ill-conditioned. Accordingly, we develop a fully automatic single-channel blind-deconvolution algorithm to improve the performance of the TLS method. The proposed algorithm, called Toeplitz-structured sparse TLS, has no assumptions about the phase of the wavelet. However, it assumes that the reflectivity series is sparse. In addition, to reduce the model space and the number of unknowns, the algorithm benefits from the structural constraints on the data matrix. Our algorithm is an alternating minimization method and uses a generalized cross validation function to define the optimum regularization parameter automatically. Because the generalized cross validation function does not require any prior information about the noise level of the data, our approach is suitable for real-world applications. We validate the proposed technique using synthetic examples. In noise-free data, we achieve a near-optimal recovery of the wavelet and the reflectivity series. For noise-corrupted data with a moderate signal-to-noise ratio (S/N), we found that the algorithm successfully accounts for the noise in its model, resulting in a satisfactory performance. However, the results deteriorate as the S/N and the sparsity level of the data are decreased. We also successfully apply the algorithm to real data. The real-data examples come from 2D and 3D data sets of the Teapot Dome seismic survey.

Sign in / Sign up

Export Citation Format

Share Document