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

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  • Liyun Su
  • Yanyong Zhao
  • Tianshun Yan
  • Fenglan Li

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.

Suggested Citation

  • Liyun Su & Yanyong Zhao & Tianshun Yan & Fenglan Li, 2012. "Local Polynomial Estimation of Heteroscedasticity in a Multivariate Linear Regression Model and Its Applications in Economics," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-13, September.
    • Handle: RePEc:plo:pone00:0043719
    DOI: 10.1371/journal.pone.0043719
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    References listed on IDEAS

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    2. Junhai Ma & Lixia Liu, 2008. "Multivariate Nonlinear Analysis and Prediction of Shanghai Stock Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-8, May.
    3. L. Galtchouk & S. Pergamenshchikov, 2009. "Sharp non-asymptotic oracle inequalities for non-parametric heteroscedastic regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 1-18.
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