THE PARAMETRIC AND NONPARAMETRIC ESTIMATOR IN SEMIPARAMETRIC REGRESSION FOR LONGITUDINAL DATA WITH SPLINE APPROACH
DOI:
https://doi.org/10.21107/kursor.v11i4.316Keywords:
Semiparametric Regression, Longitudinal Data, Spline, GCV (Generalized Cross Validation), Electricity Consumption in MaduraAbstract
Regression analysis aims to determine the relationship between response variables and predictor variables. There are three approaches to estimate regression curves, there are parametric, nonparametric, and semiparametric regression. In this study, the form of spline semiparametric regression curve estimator for longitudinal data assessed. Based on the estimator that be obtained by using Weighted Least Square (WLS) optimization applied to model electricity consumption in Madura by choosing a model for longitudinal data based on linear spline estimator with two knot. The good criterion of the model is using the GCV value, the coefficient of determination and the value of MSE. The best model is a model that has a high coefficient of determination and a small MSE value. This spline model has a determination coefficient value of 99,72911% and MSE 32,50458.
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References
[1] Fan, J. and Gijbels, I. Local Polynomial Modelling and Its Applications. London: Chapman and Hall. 1997
[2] Mardianto, M. F. F., Kartiko, S. H., and Utami, H. Forecasting Trend-Seasonal Data Using Nonparametric Regression with Kernel and Fourier Series Approach. Proceedings of the Third International Conference on Computing, Mathematics and Statistics (ICMS2017)
[3] Yani, N. W., Srinadi, I. G., & Sumarjaya, I. W. Aplikasi Model Semiparametrik Spline Truncated (Study Kasus: Pasien Demam Berdarah Dengue di Rumah Sakit Puru Raharja). E-Journal Matematika.2017
[4] Kuzairi, Miswanto, Budiantara, I., N., Three form fourier series estimator semiparametric regression for longitudinal data. Journal of Physics: Conference Series, 2020
[5] Eubank, R. L. Nonparametric Regression and Spline Smoothing (Second ed.). New York: Marcel Dekker.1999
[6] Pratiwi, D. A. Linier Spline Semiparametric Approach for The Average of Age at First Marriage in East Java. Surabaya: Undergraduate Programe Departemen of Statistic Faculty of Mathematics and Natural Science Institut Teknologi Sepuluh Nopember.2016
[7] Budiantara, I. N. Model of Truncated Polinomial Spline Family in Semiparametric Regression. Berkala MIPA, 15(3).2005
[8] Weiss, R. E. Modelling Longitudinal Data. New York: Spinger Texts in Statistic.2005
[9] Fitriana, D., Budiantara, I. N., & Ratnasari, V. Semiparametric Spline Truncated Regression on Modelling AHH in Indonesia. The 3rd International Seminar on Science and Technology (p. 26). Surabaya: Postgraduate Program Institut Teknologi Sepuluh Nopember.2017
[10] Crainiceanu, C. M. Nonparametric Regression Methods for Longitudinal Data Analysis Mixed-effects Modelling Approaches. Journal of the American Statistical Association, 102(476).2007
[11] Shim, J., & Seok, K. H. Semiparametric Kernel Logistic Regression with Longitudinal Data. Journal of the Korean Data & Information Science Society, 23(2).2012
[12] Wahba, G. Spline Model for Observational Data. SIAM XII. USA: Philadelphia. 1990
[2] Mardianto, M. F. F., Kartiko, S. H., and Utami, H. Forecasting Trend-Seasonal Data Using Nonparametric Regression with Kernel and Fourier Series Approach. Proceedings of the Third International Conference on Computing, Mathematics and Statistics (ICMS2017)
[3] Yani, N. W., Srinadi, I. G., & Sumarjaya, I. W. Aplikasi Model Semiparametrik Spline Truncated (Study Kasus: Pasien Demam Berdarah Dengue di Rumah Sakit Puru Raharja). E-Journal Matematika.2017
[4] Kuzairi, Miswanto, Budiantara, I., N., Three form fourier series estimator semiparametric regression for longitudinal data. Journal of Physics: Conference Series, 2020
[5] Eubank, R. L. Nonparametric Regression and Spline Smoothing (Second ed.). New York: Marcel Dekker.1999
[6] Pratiwi, D. A. Linier Spline Semiparametric Approach for The Average of Age at First Marriage in East Java. Surabaya: Undergraduate Programe Departemen of Statistic Faculty of Mathematics and Natural Science Institut Teknologi Sepuluh Nopember.2016
[7] Budiantara, I. N. Model of Truncated Polinomial Spline Family in Semiparametric Regression. Berkala MIPA, 15(3).2005
[8] Weiss, R. E. Modelling Longitudinal Data. New York: Spinger Texts in Statistic.2005
[9] Fitriana, D., Budiantara, I. N., & Ratnasari, V. Semiparametric Spline Truncated Regression on Modelling AHH in Indonesia. The 3rd International Seminar on Science and Technology (p. 26). Surabaya: Postgraduate Program Institut Teknologi Sepuluh Nopember.2017
[10] Crainiceanu, C. M. Nonparametric Regression Methods for Longitudinal Data Analysis Mixed-effects Modelling Approaches. Journal of the American Statistical Association, 102(476).2007
[11] Shim, J., & Seok, K. H. Semiparametric Kernel Logistic Regression with Longitudinal Data. Journal of the Korean Data & Information Science Society, 23(2).2012
[12] Wahba, G. Spline Model for Observational Data. SIAM XII. USA: Philadelphia. 1990
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