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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Universitas Pattimura
2025-01-01
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| 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. |
| format | Article |
| id | doaj-art-2d419d18c59c41d6af084060356171b3 |
| institution | DOAJ |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| 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 |
| work_keys_str_mv | AT andrefajryalbarra knotoptimizationforbiresponsesplinenonparametricregressionwithgeneralizedcrossvalidationgcv AT dewiretnosarisaputro knotoptimizationforbiresponsesplinenonparametricregressionwithgeneralizedcrossvalidationgcv |