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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Kartika Fitriasari
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Mathematics

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The Estimation of Residual Variance in Nonparametric Regression Abdul Wahab; I Nyoman Budiantara; Kartika Fitriasari
Jurnal Matematika, Statistika dan Komputasi Vol. 17 No. 3 (2021): May, 2021
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v17i3.13192

Abstract

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.
Co-Authors Abdul Wahab I Nyoman Budiantara