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Journal of Applied Mathematics
Volume 2014, Article ID 435925, 5 pages
http://dx.doi.org/10.1155/2014/435925
Research Article

Testing Heteroscedasticity in Nonparametric Regression Based on Trend Analysis

1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China
2Electronic Equipment Test Center, Luoyang 471003, China

Received 27 January 2014; Revised 26 May 2014; Accepted 26 May 2014; Published 11 June 2014

Academic Editor: Zhihua Zhang

Copyright © 2014 Si-Lian Shen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Dette, “A consistent test for heteroscedasticity in nonparametric regression based on the kernel method,” Journal of Statistical Planning and Inference, vol. 103, no. 1-2, pp. 311–329, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  2. H. Dette and A. Munk, “Testing heteroscedasticity in nonparametric regression,” Journal of the Royal Statistical Society B, vol. 60, no. 4, pp. 693–708, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  3. R. L. Eubank and W. Thomas, “Detecting heteroscedasticity in nonparametric regression,” Journal of the Royal Statistical Society B, vol. 55, no. 1, pp. 145–155, 1993. View at Google Scholar · View at MathSciNet
  4. H. Liero, “Testing homoscedasticity in nonparametric regression,” Journal of Nonparametric Statistics, vol. 15, no. 1, pp. 31–51, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. H. You and G. M. Chen, “Testing heteroscedasticity in partially linear regression models,” Statistics and Probability Letters, vol. 73, no. 1, pp. 61–70, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. H. You, G. M. Chen, and Y. Zhou, “Statistical inference of partially linear regression models with heteroscedastic errors,” Journal of Multivariate Analysis, vol. 98, no. 8, pp. 1539–1557, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  7. L. Zhang and C.-L. Mei, “Testing heteroscedasticity in nonparametric regression models based on residual analysis,” Applied Mathematics, vol. 23, no. 3, pp. 265–272, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. L. Shen, C.-L. Mei, and Y. J. Zhang, “Spatially varying coefficient models: testingfor heteroscedasticity and reweighting estimation of the coefficients,” Environmentand Planning A, vol. 43, no. 7, pp. 1723–1745, 2011. View at Google Scholar
  9. J. Q. Fan, “Design-adaptive nonparametric regression,” Journal of the American Statistical Association, vol. 87, no. 420, pp. 998–1004, 1992. View at Google Scholar · View at MathSciNet
  10. J. Q. Fan, “Local linear regression smoothers and their minimax efficiencies,” The Annals of Statistics, vol. 21, no. 1, pp. 196–216, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  11. D. Ruppert and M. P. Wand, “Multivariate locally weighted least squares regression,” The Annals of Statistics, vol. 22, no. 3, pp. 1346–1370, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  12. C. M. Hurvich, J. S. Simonoff, and C. L. Tsai, “Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion,” Journal of the Royal Statistical Society B, vol. 60, no. 2, pp. 271–293, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. D. Hart, Nonparametric Smoothing and Lack-of-Fit Tests, Springer Series in Statistics, Springer, New York, NY, USA, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  14. T. J. Hastie and R. J. Tibshirani, Generalized Additive Models, Chapman and Hall Press, London, UK, 1990. View at MathSciNet
  15. A. Diblasi and A. Bowman, “Testing for constant variance in a linear model,” Statistics and Probability Letters, vol. 33, no. 1, pp. 95–103, 1997. View at Publisher · View at Google Scholar
  16. B. C. Wei, X. G. Lin, and F. C. Xie, Statistical Diagnostics, Higher Education Press, Beijing, China, 2009. View at MathSciNet