Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014 (2014), Article ID 398082, 10 pages
http://dx.doi.org/10.1155/2014/398082
Research Article

The Local Linear -Estimation with Missing Response Data

1School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, China
2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
3Institute of Information and System Science and School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Received 18 May 2014; Accepted 7 June 2014; Published 29 June 2014

Academic Editor: Shi-Liang Wu

Copyright © 2014 Shuanghua Luo 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. J. Fan and I. Gijbels, Local Polynomial Modelling and Its Applications, Chapman and Hall, London, UK, 1996.
  2. P. J. Green and B. W. Silverman, Kernel Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, London, UK, 1994.
  3. D. M. Titterington and G. M. Mill, “Kernel-based density estimates from incomplete data,” Journal of the Royal Statistical Society B: Methodological, vol. 45, no. 2, pp. 258–266, 1983. View at Google Scholar · View at MathSciNet
  4. J. 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 Zentralblatt MATH · View at MathSciNet
  5. T. Hastie and C. Loader, “Local regression: automatic kernel estimators of regression curves,” Annals of Statistics, vol. 15, pp. 182–201, 1993. View at Google Scholar
  6. T. Orchard and M. A. Woodbury, “A missing information principle: theory and applications,” in Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, vol. 3, pp. 697–715, University of California, June-July 1970. View at MathSciNet
  7. 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 Zentralblatt MATH · View at MathSciNet
  8. P. E. Cheng, “Nonparametric estimation of mean functionals with data missing at random,” Journal of the American Statistical Association, vol. 89, no. 425, pp. 81–87, 1994. View at Publisher · View at Google Scholar
  9. K. Hirano, G. W. Imbens, and G. Ridder, “Efficient estimation of average treatment effects using the estimated propensity score,” Econometrica, vol. 71, no. 4, pp. 1161–1189, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. Q. Wang, O. Linton, and W. Härdle, “Semiparametric regression analysis with missing response at random,” Journal of the American Statistical Association, vol. 99, no. 466, pp. 334–345, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. H. Liang, “Generalized partially linear models with missing covariates,” Journal of Multivariate Analysis, vol. 99, no. 5, pp. 880–895, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. Q. Wang and Z. Sun, “Estimation in partially linear models with missing responses at random,” Journal of Multivariate Analysis, vol. 98, no. 7, pp. 1470–1493, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. J. Fan and I. Gijbels, “Variable bandwidth and local linear regression smoothers,” The Annals of Statistics, vol. 20, no. 4, pp. 2008–2036, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  14. R. J. Carroll, J. Fan, J. Gijbels, and M. P. Wand, “Generalized partially linear single-index models,” Journal of the American Statistical Association, vol. 92, no. 438, pp. 477–489, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. J. Fan and J. Jiang, “Variable bandwidth and one-step local M-estimator,” Science in China A, vol. 29, no. 1, pp. 688–702, 1999. View at Publisher · View at Google Scholar · View at Scopus