The Alternative from Regression Curve Estimation using Mixed Fourier Series and Epanechnikov Kernel (MFs-EK) Model

A.T.R. Dani¹ , L. Ni’matuzzahroh² , U.S. Nuraini³ , N.Y. Adrianingsih⁴

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.3 , pp.19-25, Jun-2022

Online published on Jun 30, 2022

Copyright © A.T.R. Dani, L. Ni’matuzzahroh, U.S. Nuraini, N.Y. Adrianingsih . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Nonparametric regression approach is generally used to avoid assumption of certain regression curve shape. Nonparametric regression has several estimators include Fourier Series (FS) and Kernel estimator. The Fourier Series estimator can adapt effectively to character of the data and kernel estimator is one of best convergence speed. In this study, the research proposed the alternative model in estimating the shape of the nonparametric regression curve using Mixed Fourier Series and Epanechnikov Kernel (MFs-EK) model. The alternative model has obtained a parameter estimate using Maximum Likelihood Estimation (MLE). Last, this study describes the estimator properties of the MFs-EK model. The proposed can be used for further analysis in nonparametric regression field.

Key-Words / Index Term :
Fouries Series Estimator, Kernel Estimator, Mixed Estimator, Nonparametric Regression

References :
[1] Rahmat Hidayat, I. Nyoman Budiantara, Bambang W. Otok, Vita Ratnasari, “The regression curve estimation by using mixed smoothing spline and kernel (MsS-K) model,” Communications in Statistics - Theory and Methods, vol. 50, no. 17, pp. 3942-3953, 2020
[2] Vita Ratnasari, I Nyoman Budiantara, 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
[3] Wolfgang Karl Härdle?, Enno Mammen, “Comparing Nonparametric Versus Parametric Regression Fits,” The Annals of Statistics, vol. 21, no. 4, pp. 1926–1947, 1993?
[4] I Nyoman Budiantara, Vita Ratnasari, Madu Ratna, Wahyu Wibowo, Ngizatul Afifah, Dyah Putri Rahmawati, Made Ayu Dwi Octavanny, “Modeling percentage of poor people in Indonesia using kernel and Fourier series mixed estimator in nonparametric regression,” Investigacion Operacional, vol. 40, no. 4, pp. 538–550, 2019
[5] Ni Putu Ayu Mirah Mariati, I. Nyoman Budiantara, Vita Ratnasari, “Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression,” Journal of Mathematics, vol. 2020, 2020
[6] Andrea Tri Rian Dani, Vita Ratnasari, I Nyoman Budiantara, “Optimal Knots Point and Bandwidth Selection in Modeling Mixed Estimator Nonparametric Regression,” IOP Conference Series: Materials Science and Engineering, vol. 1115, no. 1, p. 012020, 2021
[7] Mustain Ramli, Vita Ratnasari, Nyoman Budiantara, “Estimation of Matrix Variance-Covariance on Nonparametric Regression Spline Truncated for Longitudinal Data,” Journal of Physics: Conference Series, vol. 1562, no. 1, 2020
[8] Sifriyani, Hillidatul Ilmi, Zakiyah Mar`ah, “Application of Nonparametric Geographically Weighted Spline Regression Model for Spatial Mapping of Open Unemployment Rate in Kalimantan,” Journal of Physics: Conference Series, vol. 2123, no. 1, 2021
[9] Helida Nurcahayani, I Nyoman Budiantara, Ismaini Zain, “The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression,” Mathematics, vol. 9, no. 10, p. 1141, 2021
[10] Grace Wahba and Yuedong Wang, “Spline Function,” Encyclopedia of Statistical Sciences, pp. 1–27, 2014,
[11] Dyah Putri Rahmawati, I Nyoman Budiantara, Dedy Dwi Prastyo, Made Ayu Dwi Octavanny, “Modeling of Human Development Index in Papua Province Using Spline Smoothing Estimator in Nonparametric Regression,” Journal of Physics: Conference Series, vol. 1752, no. 1, 202
[12] Narita Yuri Adrianingsih, I Nyoman Budiantara, Jerry Dwi Trijoyo Purnomo, “Mixture Model Nonparametric Regression and Its Application,” Journal of Physics: Conference Series, vol. 1842, no. 1, pp. 012044, 2021.
[13] Made Ayu Dwi Octavanny, I Nyoman Budiantara, Heri Kuswanto, Dyah Putri Rahmawati, “Modeling of Children Ever Born in Indonesia Using Fourier Series Nonparametric Regression,” Journal of Physics: Conference Series, vol. 1752, no. 1, pp. 012019, 2021
[14] Suparti, Rukun Santoso, Alan Prahutama, Alvita Rachma Devi, “Indonesia’s Inflation Analysis Using Hybrid Fourier - Wavelet Multiscale Autoregressive Method,” Journal of Physics: Conference Series, vol. 1306, no. 1, pp. 012041, 2019
[15] I Wayan Sudiarsa, “Simulations Study Combined Estimator Fourier Series and Spline Truncated in Multivariable Nonparametric Regression,” IOP Conference Series: Materials Science and Engineering, vol. 546, no. 5, 2019, doi: 10.1088/1757-899X/546/5/052074
[16] Martin Bilodeau, “Fourier smoother and additive models,” Canadian Journal of Statistics, vol. 20, no. 3, pp. 257–269, 1992
[17] M. Fariz Fadillah Mardianto, Sri Haryatmi Kartiko, Herni Utami, “The fourier series estimator to predict the number of dengue and malaria sufferers in Indonesia,” AIP Conference Proceedings, vol. 2329, no. 1, 2021
[18] Langat Reuben Cheruiyot, “Local linear regression estimator on the boundary correction in nonparametric regression estimation,” Journal of Statistical Theory and Applications, vol. 19, no. 3, pp. 460–471, 2020
[19] Hamed Aljuhani Khulood, Lutfiah Ismail Al turk, “Modification of the adaptive Nadaraya-Watson kernel regression estimator,” Scientific Research and Essays, vol. 9, no. 22, pp. 966–971, 2014
[20] Ngizatul Afifah, I Nyoman Budiantara, I Nyoman Latra, “Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression,” Journal of Physics: Conference Series, vol. 855, no. 1, pp. 012002, 2017
[21] Zhuan Pei, David S. Lee, David Card, Andrea Weber, “Local Polynomial Order in Regression Discontinuity Designs,” Journal of Business and Economic Statistics, vol. 40, no. 3, pp. 1259–1267, 2022.
[22] Millatul Ulya, Nur Chamidah, Toha Saifudin, , “Predicting the sweetness level of avomango (Gadung Klonal 21) using multi-predictor local polynomial regression,” IOP Conference Series: Earth and Environmental Science, vol. 733, no. 1, pp. 012009, 2021
[23] Lin Liu, Rajarshi Mukherjee, James M. Robins, Eric Tchetgen Tchetgen, “Adaptive estimation of nonparametric functionals,” Journal of Machine Learning Research, vol. 22, pp. 1–66, 2021.
[24] Pedro A. Morettin, Rogério F. Porto, “Estimation of nonparametric regression models by wavelets,” Sao Paulo Journal of Mathematical Sciences, vol. 16, pp. 539-565, 2022
[25] Mohmmed Salh AbduAlkareem Mahdi, Saad Kadem Hamza, “Using the wavelet analysis to estimate the nonparametric regression model in the presence of associated errors,” Int. J. Nonlinear Anal. Appl, vol. 13, no. 1, pp. 1855–1862, 2022
[26] M. Fariz Fadillah Mardianto, Gunardi, Herni Utami, “An analysis about fourier series estimator in nonparametric regression for longitudinal data,” Mathematics and Statistics, vol. 9, no. 4, pp. 501–510, 2021
[27] Ni Putu Ayu Mirah Mariati, I. Nyoman Budiantara, Vita Ratnasari, “The application of mixed smoothing spline and fourier series model in nonparametric regression,” Symmetry (Basel), vol. 13, no. 11, pp. 2094, 202
[28] Andi Tenri Ampa, I Nyoman Budiantara, Ismaini Zain, “Selection of Optimal Smoothing Parameters in Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression,” Journal of Physics: Conference Series, vol. 2123, no. 1, p. 012035, 2021
[29] Rahmat Hidayat, I Nyoman Budiantara, Bambang Widjanarko Otok, Vita Ratnasari, “Kernel-Spline Estimation of Additive Nonparametric Regression Model,” IOP Conference Series: Materials Science and Engineering, vol. 546, no. 5, 2019
[30] I. Nyoman Budiantara, Vita Ratnasari, Madu Ratna, Ismaini Zain, “The Combination of Spline and Kernel Estimator for Nonparametric Regression and its Properties,” Applied Mathematical Sciences, vol. 9, pp. 6083–6094, 2015
[31] Vita Ratnasari, I Nyoman Budiantara, Madu Ratna, Ismaini Zain, “Estimation of nonparametric regression curve using mixed estimator of multivariable truncated Spline and multivariable Kernel,” Global Journal of Pure and Applied Mathematics, vol. 12, no. 6, pp. 5047–5057, 2016
[32] Arip Ramadan, I Nyoman Budiantara, Ismaini Zain, “Modeling of Total Fertility Rate (TFR) in East Java Province using Mixed Semiparametric Regression Spline Truncated and Kernel Approach,” Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pp. 271–277, 2018
[33] Dyah Putri Rahmawati, I. Nyoman Budiantara, Dedy Dwi Prastyo, Made Ayu Dwi Octavanny, “Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression,” International Journal of Mathematics and Mathematical Sciences, vol. 2021, 2021
[34] I. Wayan Sudiarsa, Suhartono, Santi Wulan Purnami, “Combined estimator fourier series and spline truncated in multivariable nonparametric regression,” Applied Mathematical Sciences, vol. 9, pp. 4997–5010, 2015.