The Estimation of Residual Variance in Nonparametric Regression
| Main Authors: | Wahab, Abdul, Budiantara, I Nyoman , Fitriasari, Kartika |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
Department of Mathematics, Hasanuddin University
, 2021
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| Subjects: | |
| Online Access: |
https://journal.unhas.ac.id/index.php/jmsk/article/view/13192 https://journal.unhas.ac.id/index.php/jmsk/article/view/13192/6715 |
Daftar Isi:
- Given a nonparametric regression model Yi = g(xi) + ei, i = 1, 2, ..., n, where Y is a dependent variable, x is an independent variable, g is an unknown function and e is an error assumed to be an independent, identical, and is distributed with mean 0 and variance σ2. In this research Rice estimator is used to determine the biased value of a residual variance estimator. The Rice estimator is given as follows: . The biased value of residual variance estimator of the Rice method is: , where and. Using the Rice estimator, the Tong-Wang residual variance estimator is obtained, that is: , Where , , , , , k = 1, 2, ... , m. Based upon the data simulation by considering the exponential, arithmetical, and trigonometrical models, it is found that the MSE value of the Tong-Wang estimator tends to be less compared to those of the Rice estimator as well as the GSJ (Gasser, Sroka, and Jennen) estimator.
- Diberikan model regresi nonparametrik Yi = g(xi) + ei, i = 1, 2, ..., n, dengan Y adalah variabel dependen, x variabel independen, g fungsi yang tidak ditetapkan bentuknya dan e eror yang diasumsikan independen, identik dan berdistribusi dengan rataan 0 dan varians σ2. Dalam penelitian ini digunakan penduga Rice untuk mendapatkan nilai bias penduga varians residual. Penduga Rice diberikan oleh: . Nilai bias penduga varians residual metode Rice adalah: , dimana dan . Dengan menggunakan penduga Rice diperoleh penduga varians residual Tong-Wang yaitu: , dimana , , , , , k = 1, 2, ... , m. Berdasarkan data simulasi dengan mempertimbangkan model eksponensial, aritmetika dan trigonometri diperoleh nilai MSE penduga Tong-Wang cenderung lebih kecil dibandingkan dengan penduga Rice dan penduga GSJ (Gasser, Sroka, dan Jennen).