Local Polynomial Estimation of Heteroscedasticity in a Multivariate Linear Regression Model and Its Applications in Economics

Liyun Su,Fenglan Li,Yanyong Zhao,Tianshun Yan,Timothy Ravasi

doi:10.1371/journal.pone.0043719

Liyun Su, Fenglan Li + Show 3 more

Open Access

https://doi.org/10.1371/journal.pone.0043719

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Journal: PLoS ONE	Publication Date: Sep 17, 2012
Citations: 32	License type: CC BY 4.0

Affiliation: Chongqing University of Technology

Abstract

Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.

Highlights

The heteroscedasticity in classical linear regression model is defined by the variances of random items and which are not the same for different explanatory variables and observations [1,2]
We try to apply multivariate local polynomial fitting to random item variances as the first step, and generalized least squares estimation is used to estimate the coefficients of the model
The multivariate local polynomial estimation adopted is explained in detail in Section Methods [16,17,18]: in its the first Subsection we study multivariate estimation with local polynomial fitting

Summary

Introduction

The heteroscedasticity in classical linear regression model is defined by the variances of random items and which are not the same for different explanatory variables and observations [1,2]. The efficiency is bad [11,12] This could lead to a uncorrect statistical diagnosis for the parameters’ significance test. In order to solve the problem above, we can use generalized least squares estimation (GLS) when the covariance matrix of the random items is known. If it is unknown, we usually use two-stage least squares estimate. We try to apply multivariate local polynomial fitting to random item variances as the first step, and generalized least squares estimation is used to estimate the coefficients of the model. The estimated value by multivariate local polynomial fitting are more accurate than that by the traditional method and univariate local polynomial fitting

Methods

Results

Conclusion