Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods
How to cite (IJASEIT) :
A. T. R. Dani, V. Ratnasari, and I. N. Budiantara, “Optimal Knots Point and Bandwidth Selection in Modeling Mixed Estimator Nonparametric Regression,” IOP Conf. Ser. Mater. Sci. Eng., vol. 1115, no. 1, p. 012020, 2021, doi: 10.1088/1757-899x/1115/1/012020.
R. L. Eubank, Nonparametric Regression and Spline Smoothing, New York: Marcel Dekker, 1999.
I. N. Budiantara, V. Ratnasari, M. Ratna, and I. Zain, “The Combination of Spline and Kernel Estimator for Nonparametric Regression and its Properties,” Appl. Math. Sci., vol. 9, no. 122, pp. 6083-6094, 2015, doi: 10.12988/ams.2015.58517.
N. Y. Adrianingsih, I. N. Budiantara, and J. D. T. Purnomo, “Modeling with Mixed Kernel, Spline Truncated and Fourier Series on Human Development Index in East Java,” IOP Conf. Ser. Mater. Sci. Eng., vol. 1115, no. 1, p. 012024, 2021, doi: 10.1088/1757-899x/1115/1/012024.
D. R. Sari Saputro, K. R. Demu, and P. Widyaningsih, “Nonparametric truncated spline regression model on the data of human development index (HDI) in indonesia,” J. Phys. Conf. Ser., vol. 1028, no. 1, pp. 6-10, 2018, doi: 10.1088/1742-6596/1028/1/012219.
N. Chamidah, B. Lestari, A. Massaid, and T. Saifudin, “Estimating mean arterial pressure affected by stress scores using Spline Nonparametric Regression model approach,” Commun. Math. Biol. Neurosci., vol. 2020, pp. 1-12, 2020.
G. Wahba, Spline Models for Observational Data, Pennsylvania: SIAM, 1990.
N. P. A. M. Mariati, N. Budiantara, and V. Ratnasari, “Truncated Spline Estimation of Percentage Poverty Modeling in Papua Province,” ICSA - Int. Conf. Stat. Anal. 2019, vol. 1, pp. 69-82, 2021, doi: 10.29244/icsa.2019.pp69-82.
B. Fatmawati, Budiantara, I N; Lestari, “Comparison of Smoothing and Truncated Spline Estimators in Estimating Blood Pressure Models,” Int. J. Innov. Creat. Chang., vol. 5, no. 3, pp. 685-707, 2019.
N. P. A. M. Mariati, I. N. Budiantara, and V. Ratnasari, “Smoothing Spline Estimator in Nonparametric Regression (Application: Poverty in Papua Province),” Proc. 7th Int. Conf. Res. Implementation, Educ. Math. Sci. (ICRIEMS 2020), vol. 528, no. Icriems 2020, pp. 309-314, 2021, doi: 10.2991/assehr.k.210305.044.
B. Lestari, Fatmawati, and I. N. Budiantara, “Spline estimator and its asymptotic properties in multiresponse nonparametric regression model,” Songklanakarin J. Sci. Technol., vol. 42, no. 3, pp. 533-548, 2020, doi: 10.14456/sjst-psu.2020.68.
L. R. Cheruiyot, “Local linear regression estimator on the boundary correction in nonparametric regression estimation,” J. Stat. Theory Appl., vol. 19, no. 3, pp. 460-471, 2020, doi: 10.2991/jsta.d.201016.001.
R. Hidayat, I. N. Budiantara, B. W. Otok, and V. Ratnasari, “An extended model of penalized spline with the addition of Kernel Functions in nonparametric regression model,” Appl. Math. Inf. Sci., vol. 13, no. 3, pp. 453-460, 2019, doi: 10.18576/amis/130318.
F. Yan, Q. S. Xu, M. L. Tang, and Z. Chen, “Kernel density-based likelihood ratio tests for linear regression models,” Stat. Med., vol. 40, no. 1, pp. 119-132, 2021, doi: 10.1002/sim.8765.
N. Chamidah and T. Saifudin, “Estimation of children growth curve based on kernel smoothing in multi-response nonparametric regression,” Appl. Math. Sci., vol. 7, no. 37-40, pp. 1839-1847, 2013, doi: 10.12988/ams.2013.13168.
I. Wayan Sudiarsa, “Simulations Study Combined Estimator Fourier Series and Spline Truncated in Multivariable Nonparametric Regression,” IOP Conf. Ser. Mater. Sci. Eng., vol. 546, no. 5, 2019, doi: 10.1088/1757-899X/546/5/052074.
D. R. S. Saputro, A. Sukmayanti, and P. Widyaningsih, “The nonparametric regression model using Fourier series approximation and penalized least squares (PLS) (case on data proverty in East Java),” J. Phys. Conf. Ser., vol. 1188, no. 1, 2019, doi: 10.1088/1742-6596/1188/1/012019.
A. Prahutama, Suparti, and T. W. Utami, “Modelling fourier regression for time series data - A case study: Modelling inflation in foods sector in Indonesia,” J. Phys. Conf. Ser., vol. 974, no. 1, pp. 0-9, 2018, doi: 10.1088/1742-6596/974/1/012067.
M. F. F. Mardianto, S. M. Ulyah, and E. Tjahjono, “Prediction of national strategic commodities production based on multi-Response nonparametric regression with fourier series estimator,” Int. J. Innov. Creat. Chang., vol. 5, no. 3, pp. 1151-1176, 2019.
I. Nyoman Budiantara et al., “Modeling percentage of poor people in Indonesia using kernel and Fourier series mixed estimator in nonparametric regression,” Investig. Operacional, vol. 40, no. 4, pp. 538-550, 2019, doi: 10.5281/zenodo.3721293.
R. Hidayat, I. N. Budiantara, B. W. Otok, and V. Ratnasari, “A reproducing kernel hilbert space approach and smoothing parameters selection in spline-kernel regression,” J. Theor. Appl. Inf. Technol., vol. 97, no. 2, pp. 465-475, 2019.
R. Hidayat, I. N. Budiantara, B. W. Otok, and V. Ratnasari, “Kernel-Spline Estimation of Additive Nonparametric Regression Model,” IOP Conf. Ser. Mater. Sci. Eng., vol. 546, no. 5, 2019, doi: 10.1088/1757-899X/546/5/052028.
P. Dewanti, I. Nyoman Budiantara, and A. T. Rumiati, “Modelling of SDG’s Achievement in East Java Using Bi-responses Nonparametric Regression with Mixed Estimator Spline Truncated and Kernel,” J. Phys. Conf. Ser., vol. 1562, no. 1, 2020, doi: 10.1088/1742-6596/1562/1/012016.
D. P. Rahmawati, I. N. Budiantara, D. D. Prastyo, and M. A. D. Octavanny, “Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression,” Int. J. Math. Math. Sci., vol. 2021, 2021, doi: 10.1155/2021/6611084.
P. Craven and G. Wahba, “Smoothing noisy data with spline functions - Estimating the correct degree of smoothing by the method of generalized cross-validation,” Numer. Math., vol. 31, no. 4, pp. 377-403, 1978, doi: 10.1007/BF01404567.
Y. Wang, “Smoothing spline models with correlated random errors,” J. Am. Stat. Assoc., vol. 93, no. 441, pp. 341-348, 1998, doi: 10.1080/01621459.1998.10474115.
H. Nurcahayani, I. N. Budiantara, and I. Zain, “The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression,” Mathematics, vol. 9, no. 10, p. 1141, 2021.
A. R. Devi, I. N. Budiantara, and V. Ratnasari, “Unbiased risk and cross-validation method for selecting optimal knots in multivariable nonparametric regression spline truncated (case study: Unemployment rate in Central Java, Indonesia, 2015),” AIP Conf. Proc., vol. 2021, no. December, 2018, doi: 10.1063/1.5062767.
T. W. Utami, M. A. Haris, A. Prahutama, and E. A. Purnomo, “Optimal knot selection in spline regression using unbiased risk and generalized cross validation methods,” J. Phys. Conf. Ser., vol. 1446, no. 1, 2020, doi: 10.1088/1742-6596/1446/1/012049.
B. A. M. Al-Talib and A. A. Hammodat, “Using Some Wavelet Shrinkage Techniques and Robust Methods to Estimate the Generalized Additive Model Parameters in Non-Linear Models,” Int. J. Adv. Sci. Eng. Inf. Technol., vol. 10, no. 6, p. 2344, 2020, doi: 10.18517/ijaseit.10.6.12767.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).