The Estimation of Residual Variance in Nonparametric Regression

Authors

  • Abdul Wahab Universitas Muslim Indonesia
  • I Nyoman Budiantara
  • Kartika Fitriasari

DOI:

https://doi.org/10.20956/j.v17i3.13192

Keywords:

Nonparametric regression, Rice estimator, GSJ estimator, Tong-Wang estimator

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.

References

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Published

2021-05-12

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Section

Research Articles