Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression
So far, most of the researchers developed one type of estimator in nonparametric regression. But in reality, in daily life, data with mixed patterns were often encountered, especially data patterns which partly changed at certain subintervals, and some others followed a recurring pattern in a certai...
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/4712531 |
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| author | Ni Putu Ayu Mirah Mariati I. Nyoman Budiantara Vita Ratnasari |
| author_facet | Ni Putu Ayu Mirah Mariati I. Nyoman Budiantara Vita Ratnasari |
| author_sort | Ni Putu Ayu Mirah Mariati |
| collection | DOAJ |
| description | So far, most of the researchers developed one type of estimator in nonparametric regression. But in reality, in daily life, data with mixed patterns were often encountered, especially data patterns which partly changed at certain subintervals, and some others followed a recurring pattern in a certain trend. The estimator method used for the data pattern was a mixed estimator method of smoothing spline and Fourier series. This regression model was approached by the component smoothing spline and Fourier series. From this process, the mixed estimator was completed using two estimation stages. The first stage was the estimation with penalized least squares (PLS), and the second stage was the estimation with least squares (LS). Those estimators were then implemented using simulated data. The simulated data were gained by generating two different functions, namely, polynomial and trigonometric functions with the size of the sample being 100. The whole process was then repeated 50 times. The experiment of the two functions was modeled using a mixture of the smoothing spline and Fourier series estimators with various smoothing and oscillation parameters. The generalized cross validation (GCV) minimum was selected as the best model. The simulation results showed that the mixed estimators gave a minimum (GCV) value of 11.98. From the minimum GCV results, it was obtained that the mean square error (MSE) was 0.71 and R2 was 99.48%. So, the results obtained indicated that the model was good for a mixture estimator of smoothing spline and Fourier series. |
| format | Article |
| id | doaj-art-7ada1a2668f04517a5686057d2724e1a |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7ada1a2668f04517a5686057d2724e1a2025-02-03T06:06:55ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/47125314712531Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric RegressionNi Putu Ayu Mirah Mariati0I. Nyoman Budiantara1Vita Ratnasari2Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaDepartment of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaDepartment of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaSo far, most of the researchers developed one type of estimator in nonparametric regression. But in reality, in daily life, data with mixed patterns were often encountered, especially data patterns which partly changed at certain subintervals, and some others followed a recurring pattern in a certain trend. The estimator method used for the data pattern was a mixed estimator method of smoothing spline and Fourier series. This regression model was approached by the component smoothing spline and Fourier series. From this process, the mixed estimator was completed using two estimation stages. The first stage was the estimation with penalized least squares (PLS), and the second stage was the estimation with least squares (LS). Those estimators were then implemented using simulated data. The simulated data were gained by generating two different functions, namely, polynomial and trigonometric functions with the size of the sample being 100. The whole process was then repeated 50 times. The experiment of the two functions was modeled using a mixture of the smoothing spline and Fourier series estimators with various smoothing and oscillation parameters. The generalized cross validation (GCV) minimum was selected as the best model. The simulation results showed that the mixed estimators gave a minimum (GCV) value of 11.98. From the minimum GCV results, it was obtained that the mean square error (MSE) was 0.71 and R2 was 99.48%. So, the results obtained indicated that the model was good for a mixture estimator of smoothing spline and Fourier series.http://dx.doi.org/10.1155/2020/4712531 |
| spellingShingle | Ni Putu Ayu Mirah Mariati I. Nyoman Budiantara Vita Ratnasari Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression Journal of Mathematics |
| title | Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression |
| title_full | Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression |
| title_fullStr | Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression |
| title_full_unstemmed | Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression |
| title_short | Combination Estimation of Smoothing Spline and Fourier Series in Nonparametric Regression |
| title_sort | combination estimation of smoothing spline and fourier series in nonparametric regression |
| url | http://dx.doi.org/10.1155/2020/4712531 |
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