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

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 The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2094
Author(s):  
Ni Putu Ayu Mirah Mariati ◽  
I. Nyoman Budiantara ◽  
Vita Ratnasari
Keyword(s):  
Fourier Series ◽  
Nonparametric Regression ◽  
Simulation Study ◽  
Random Error ◽  
Cross Validation ◽  
Daily Life ◽  
Mixed Data ◽  
Smoothing Spline ◽  
Poor Households ◽  
Mixed Estimator

In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.

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>

Item Bias Analysis of the Young Schema-Questionnaire for Psychopathology, Gender, and Educational Level

2011 ◽  
Vol 27 (1) ◽  
pp. 65-70 ◽  
Author(s):  
Marleen M. Rijkeboer ◽  
Huub van den Bergh ◽  
Jan van den Bout
Keyword(s):  
Educational Level ◽  
Cross Validation ◽  
Item Bias ◽  
Response Patterns ◽  
Dutch Population ◽  
Bias Analysis ◽  
Young Schema Questionnaire ◽  
Item Functioning ◽  
Item Level ◽  
Schema Questionnaire

This study examines the construct validity of the Young Schema-Questionnaire at the item level in a Dutch population. Possible bias of items in relation to the presence or absence of psychopathology, gender, and educational level was analyzed, using a cross-validation design. None of the items of the YSQ exhibited differential item functioning (DIF) for gender, and only one item showed DIF for educational level. Furthermore, item bias analysis did not identify DIF for the presence or absence of psychopathology in as much as 195 of the 205 items comprising the YSQ. Ten items, however, spread over the questionnaire, were found to yield relatively inconsistent response patterns for patients and nonclinical participants.

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