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Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods

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@article{IJASEIT14464,
   author = {Vita Ratnasari and I Nyoman Budiantara and Andrea Tri Rian Dani},
   title = {Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods},
   journal = {International Journal on Advanced Science, Engineering and Information Technology},
   volume = {11},
   number = {6},
   year = {2021},
   pages = {2400--2406},
   keywords = {Cross-validation; generalized cross-validation; mixed estimators; unbiased risk.},
   abstract = {

Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R2) value and better accuracy for each combination of sample sizes and variance variations.

},    issn = {2088-5334},    publisher = {INSIGHT - Indonesian Society for Knowledge and Human Development},    url = {http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=14464},    doi = {10.18517/ijaseit.11.6.14464} }

EndNote

%A Ratnasari, Vita
%A Budiantara, I Nyoman
%A Dani, Andrea Tri Rian
%D 2021
%T Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods
%B 2021
%9 Cross-validation; generalized cross-validation; mixed estimators; unbiased risk.
%! Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods
%K Cross-validation; generalized cross-validation; mixed estimators; unbiased risk.
%X 

Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R2) value and better accuracy for each combination of sample sizes and variance variations.

%U http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=14464 %R doi:10.18517/ijaseit.11.6.14464 %J International Journal on Advanced Science, Engineering and Information Technology %V 11 %N 6 %@ 2088-5334

IEEE

Vita Ratnasari,I Nyoman Budiantara and Andrea Tri Rian Dani,"Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods," International Journal on Advanced Science, Engineering and Information Technology, vol. 11, no. 6, pp. 2400-2406, 2021. [Online]. Available: http://dx.doi.org/10.18517/ijaseit.11.6.14464.

RefMan/ProCite (RIS)

TY  - JOUR
AU  - Ratnasari, Vita
AU  - Budiantara, I Nyoman
AU  - Dani, Andrea Tri Rian
PY  - 2021
TI  - Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods
JF  - International Journal on Advanced Science, Engineering and Information Technology; Vol. 11 (2021) No. 6
Y2  - 2021
SP  - 2400
EP  - 2406
SN  - 2088-5334
PB  - INSIGHT - Indonesian Society for Knowledge and Human Development
KW  - Cross-validation; generalized cross-validation; mixed estimators; unbiased risk.
N2  - 

Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R2) value and better accuracy for each combination of sample sizes and variance variations.

UR - http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=14464 DO - 10.18517/ijaseit.11.6.14464

RefWorks

RT Journal Article
ID 14464
A1 Ratnasari, Vita
A1 Budiantara, I Nyoman
A1 Dani, Andrea Tri Rian
T1 Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods
JF International Journal on Advanced Science, Engineering and Information Technology
VO 11
IS 6
YR 2021
SP 2400
OP 2406
SN 2088-5334
PB INSIGHT - Indonesian Society for Knowledge and Human Development
K1 Cross-validation; generalized cross-validation; mixed estimators; unbiased risk.
AB 

Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R2) value and better accuracy for each combination of sample sizes and variance variations.

LK http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=14464 DO - 10.18517/ijaseit.11.6.14464