KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)

Nonparametric regression is a statistical method used to model relationships between variables without making strong assumptions about the functional form of the relationship. Nonparametric regression models are flexible and can capture complex relationships that may not be adequately represented by...

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Main Authors: Andre Fajry Al Barra, Dewi Retno Sari Saputro
Format: Article
Language:English
Published: Universitas Pattimura 2025-01-01
Series:Barekeng
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Online Access:https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13474
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author Andre Fajry Al Barra
Dewi Retno Sari Saputro
author_facet Andre Fajry Al Barra
Dewi Retno Sari Saputro
author_sort Andre Fajry Al Barra
collection DOAJ
description Nonparametric regression is a statistical method used to model relationships between variables without making strong assumptions about the functional form of the relationship. Nonparametric regression models are flexible and can capture complex relationships that may not be adequately represented by simple parametric forms. Spline is one of the approaches used in nonparametric regression. Splines have the disadvantage of having to use optimal nodes in the data. Therefore, this article discusses the retrieval of optimal knot points using the generalized cross-validation method in the nonparametric bi-response spline regression model. The research results showed that the generalized-cross validation method is the best method for selecting nodes from other methods such as CV, AIC, BIC, RSS, or a more explicit validation-based approach method because of the development of the Cross Validation (CV) method which automatically selects the optimal number of nodes based on the balance between bias and variance. The process of optimizing knot points with Generalized Cross Validation (GCV) on bi-response spline nonparametric regression is implemented using Python can provide optimization at optimal knot points. Based on the results of the generalized cross-validation model analysis, it is concluded that GCV can effectively optimize knot points for spline fitting, ensuring a balanced and efficient model in capturing data patterns without overfitting.
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spelling doaj-art-2d419d18c59c41d6af084060356171b32025-08-20T03:02:44ZengUniversitas PattimuraBarekeng1978-72272615-30172025-01-0119127128010.30598/barekengvol19iss1pp271-28013474KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)Andre Fajry Al Barra0Dewi Retno Sari Saputro1Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, IndonesiaNonparametric regression is a statistical method used to model relationships between variables without making strong assumptions about the functional form of the relationship. Nonparametric regression models are flexible and can capture complex relationships that may not be adequately represented by simple parametric forms. Spline is one of the approaches used in nonparametric regression. Splines have the disadvantage of having to use optimal nodes in the data. Therefore, this article discusses the retrieval of optimal knot points using the generalized cross-validation method in the nonparametric bi-response spline regression model. The research results showed that the generalized-cross validation method is the best method for selecting nodes from other methods such as CV, AIC, BIC, RSS, or a more explicit validation-based approach method because of the development of the Cross Validation (CV) method which automatically selects the optimal number of nodes based on the balance between bias and variance. The process of optimizing knot points with Generalized Cross Validation (GCV) on bi-response spline nonparametric regression is implemented using Python can provide optimization at optimal knot points. Based on the results of the generalized cross-validation model analysis, it is concluded that GCV can effectively optimize knot points for spline fitting, ensuring a balanced and efficient model in capturing data patterns without overfitting.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13474bi-responsegcvknot pointnonparametric regressionspline
spellingShingle Andre Fajry Al Barra
Dewi Retno Sari Saputro
KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)
Barekeng
bi-response
gcv
knot point
nonparametric regression
spline
title KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)
title_full KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)
title_fullStr KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)
title_full_unstemmed KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)
title_short KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)
title_sort knot optimization for bi response spline nonparametric regression with generalized cross validation gcv
topic bi-response
gcv
knot point
nonparametric regression
spline
url https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13474
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