scholarly journals Generalized Cross Validation (GCV) in Smoothing Spline Nonparametric Regression Models

2021 ◽  
Vol 1808 (1) ◽  
pp. 012053
Author(s):  
M Maharani ◽  
D R S Saputro
Keyword(s):  
Nonparametric Regression ◽  
Regression Models ◽  
Cross Validation ◽  
Smoothing Spline ◽  
Generalized Cross Validation

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>

scholarly journals Model Regresi Nonparametrik dengan Pendekatan Spline (Studi Kasus: Berat Badan Lahir Rendah di Rumah Sakit Ibu dan Anak Siti Fatimah Makassar)

2020 ◽  
Vol 2 (1) ◽  
pp. 70
Author(s):  
Wahidah Sanusi ◽  
Rahmat Syam ◽  
Rabiatul Adawiyah
Keyword(s):  
Birth Weight ◽  
Low Birth Weight ◽  
Nonparametric Regression ◽  
Gestational Age ◽  
Cross Validation ◽  
Predictor Variable ◽  
Coefficient Of Determination ◽  
Generalized Cross Validation ◽  
Child Hospital ◽  
The Relationship

Pendekatan nonparametrik merupakan suatu pendekatan yang digunakan apabila bentuk hubungan antara variabel respon dan variabel prediktornya tidak diketahui atau tidak adanya informasi mengenai bentuk fungsi regresinya. Spline merupakan suatu teknik yang dilakukan untuk mengestimasi parameter dalam regresi nonparametrik. Penelitian ini bertujuan untuk mengetahui model hubungan antara berat badan lahir rendah dan faktor-faktor yang mempengaruhi berdasarkan model spline. Faktor-faktor tersebut adalah usia ibu, usia kehamilan, dan jarak kehamilan. Data tersebut diperoleh dari rumah sakit ibu dan anak siti Fatimah Makassar tahun 2017. Dimana untuk mendapatkan model spline terbaik langkah awal yang dilakukan adalah menentukan knot dengan nilai Generalized Cross Validation (GCV) yang minimum. Berdasarkan penelitian yang telah dilakukan, dua variabel dinyatakan berpengaruh terhadap berat badan lahir rendah yaitu usia ibu, dan usia kehamilan. Model regresi nonparametrik dengan pendekatan Spline yang terbentuk memiliki koefisien determinasi sebesar 78,19%, serta nilai GCV dengan tiga titik knot yaitu 0.0117.Kata kunci: Regresi Nonparametrik, Spline, Berat Badan Lahir Rendah, Generalized Cross Validation The non-parametric approach is an approach that is used if the form of the relationship between the response variable and the predictor variable is unknown or the absence of information about the shapes of regression functions. The Spline is a technique performed to estimate the parameters in the nonparametric regression. This study aims to determine the model of the relationship between low birth weight and the factors that affect the based on the spline model. Such factors are maternal age, gestational age, and pregnancy distance. The Data is obtained from the mother and child hospital siti Fatimah Makassar 2017. Where to get a spline model best the initial step is to determine the knots with the value of the Generalized Cross Validation (GCV) which is a minimum. Based on the research that has been done, the two variables stated effect against low birth weight, namely age of mother, and gestational age. Nonparametric regression Model with the approach of the Spline that is formed has a coefficient of determination of 78.19 to%, as well as the value of the GCV with a three-point knot that is 0.0117.Keyword : Nonparametric Regression, Spline, Low Birth Weight, Generalized Cross Validation

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 PEMODELAN RATA-RATA LAMA SEKOLAH MENGGUNAKAN PENDEKATAN REGRESI NONPARAMETRIK SPLINE MULTIVARIABLE

2021 ◽  
Vol 10 (2) ◽  
pp. 53
Author(s):  
NI LUH GEDE SINTA ARYATI ◽  
I KOMANG GDE SUKARSA ◽  
I GUSTI AYU MADE SRINADI
Keyword(s):  
Human Development ◽  
Nonparametric Regression ◽  
Human Development Index ◽  
Cross Validation ◽  
Development Index ◽  
Generalized Cross Validation ◽  
Minimum Value

Mean years school (MYS) is one of the indicators used in calculating the human development index (HDI). The value of MYS Indonesia in 2019 is 8,75 which is still low. Therefore it still needs to be improved. In this research, MYS modeling will be carried out using six factors that are thought to influence MYS. This research uses multivariable spline nonparametric regression to modeling MYS Indonesia in 2019. The best model is selected based on the minimum value of Generalized Cross Validation (GCV). Based on this research, the best model obtained is a linear orde (orde 2) spline model with four knots. The model has    value of  99,91%.

scholarly journals Goodness-of-fit test for nonparametric regression models: Smoothing spline ANOVA models as example

2018 ◽  
Vol 122 ◽  
pp. 135-155 ◽  
Author(s):  
Sebastian J. Teran Hidalgo ◽  
Michael C. Wu ◽  
Stephanie M. Engel ◽  
Michael R. Kosorok
Keyword(s):  
Nonparametric Regression ◽  
Regression Models ◽  
Goodness Of Fit ◽  
Smoothing Spline ◽  
Goodness Of Fit Test ◽  
Smoothing Spline Anova

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.

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