Cross-validation techniques for smoothing spline functions in one or two dimensions

1979 ◽  
pp. 196-232 ◽  
Author(s):  
F. Utreras
Keyword(s):  
Cross Validation ◽  
Two Dimensions ◽  
Smoothing Spline ◽  
Spline Functions

scholarly journals The Study of Light Curves with the Aid of Smoothing Spline-Functions

1975 ◽  
Vol 67 ◽  
pp. 567-569
Author(s):  
V. Pop ◽  
P. Pop
Keyword(s):  
Light Curve ◽  
Light Curves ◽  
Smoothing Spline ◽  
Spline Functions

By means of smoothing spline functions an attempt is made to approximate cepheid-type light curves. As an example the light curve of XZ Cyg is used.

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.

An algorithm for computing constrained smoothing spline functions

1987 ◽  
Vol 52 (5) ◽  
pp. 583-595 ◽  
Author(s):  
Tommy Elfving ◽  
Lars-Erik Andersson
Keyword(s):  
Smoothing Spline ◽  
Spline Functions

The Na+, K+/CN-, I- binary systems

1990 ◽  
Vol 55 (7) ◽  
pp. 1741-1749
Author(s):  
Milan Drátovský ◽  
Bohumír Grüner ◽  
Ivan Horsák ◽  
Jiří Makovička
Keyword(s):  
Phase Diagram ◽  
Binary System ◽  
Phase Diagrams ◽  
Solid Solutions ◽  
Binary Systems ◽  
Smoothing Spline ◽  
Spline Functions ◽  
Solidus Curve

The phase diagram of the KCN-KI binary system was measured and the published phase diagrams of the KCN-NaCN, NaI-KI and NaCN-NaI systems were verified and completed. The systems form solid solutions with minima on the liquidus and solidus curves. The solid solutions in the KCN-KI system probably have a high segregation temperature, close to the solidus curve. For the four binary systems the experimental points were fitted with liquidus and solidus curves either by applying smoothing spline functions or by using two different models. The results obtained are discussed.

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.

AnL 1 smoothing spline algorithm with cross validation

1993 ◽  
Vol 5 (8) ◽  
pp. 407-417 ◽  
Author(s):  
Ken W. Bosworth ◽  
Upmanu Lall
Keyword(s):  
Cross Validation ◽  
Smoothing Spline
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