Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2014), Article ID 398082, 10 pages.

The Local Linear M-Estimation with Missing Response Data

Shuanghua Luo, Cheng-Yi Zhang, and Fengmin Xu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper studies the nonparametric regressive function with missing response data. Three local linear M-estimators with the robustness of local linear regression smoothers are presented such that they have the same asymptotic normality and consistency. Then finite-sample performance is examined via simulation studies. Simulations demonstrate that the complete-case data M-estimator is not superior to the other two local linear M-estimators.

Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 398082, 10 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425050706

Digital Object Identifier
doi:10.1155/2014/398082

Mathematical Reviews number (MathSciNet)
MR3230571

Citation

Luo, Shuanghua; Zhang, Cheng-Yi; Xu, Fengmin. The Local Linear $M$ -Estimation with Missing Response Data. J. Appl. Math. 2014, Special Issue (2014), Article ID 398082, 10 pages. doi:10.1155/2014/398082. https://projecteuclid.org/euclid.jam/1425050706


Export citation

References

  • J. Fan and I. Gijbels, Local Polynomial Modelling and Its Applications, Chapman and Hall, London, UK, 1996.
  • P. J. Green and B. W. Silverman, Kernel Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, London, UK, 1994.
  • 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.
  • J. Fan, “Local linear regression smoothers and their minimax efficiencies,” The Annals of Statistics, vol. 21, no. 1, pp. 196–216, 1993.
  • T. Hastie and C. Loader, “Local regression: automatic kernel estimators of regression curves,” Annals of Statistics, vol. 15, pp. 182–201, 1993.
  • 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.
  • D. Ruppert and M. P. Wand, “Multivariate locally weighted least squares regression,” The Annals of Statistics, vol. 22, no. 3, pp. 1346–1370, 1994.
  • 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.
  • 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.
  • 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.
  • H. Liang, “Generalized partially linear models with missing covariates,” Journal of Multivariate Analysis, vol. 99, no. 5, pp. 880–895, 2008.
  • 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.
  • J. Fan and I. Gijbels, “Variable bandwidth and local linear regression smoothers,” The Annals of Statistics, vol. 20, no. 4, pp. 2008–2036, 1992.
  • 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.
  • 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. \endinput