The Estimation of Residual Variance in Nonparametric Regression (Jurnal Matematika, Statistika dan Komputasi, 2021)
Given a nonparametric regression modelYi = 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.
Keywords: Nonparametric regression; Rice estimator; GSJ estimator; Tong-Wang estimator