The Estimation of Residual Variance in Nonparametric Regression
DOI:
https://doi.org/10.20956/j.v17i3.13192Keywords:
Nonparametric regression, Rice estimator, GSJ estimator, Tong-Wang estimatorAbstract
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.
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