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On an asymptotically more efficient estimation of the single-index model

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  • Chang, Ziqing
  • Xue, Liugen
  • Zhu, Lixing

Abstract

In this note, we revisit the single-index model with heteroscedastic error, and recommend an estimating equation method in terms of transferring restricted least squares to unrestricted least squares: the estimator of the index parameter is asymptotically more efficient than existing estimators in the literature in the sense that it is of a smaller limiting variance.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 101 (2010)
Issue (Month): 8 (September)
Pages: 1898-1901

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Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1898-1901

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Related research

Keywords: The single-index model Asymptotical efficiency Least squares estimation;

References

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  1. repec:wop:humbsf:1994-36 is not listed on IDEAS
  2. Yingcun Xia & Howell Tong & W. K. Li & Li-Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410.
  3. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 97(5), pages 1162-1184, May.
  4. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
  5. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 97(6), pages 1295-1312, July.
  6. Peter Hall & Qiwei Yao, 2005. "Approximating conditional distribution functions using dimension reduction," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 16333, London School of Economics and Political Science, LSE Library.
  7. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single-index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570.
  8. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1112-1137, December.
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Citations

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Cited by:
  1. Guo, Xu & Xu, Wangli & Zhu, Lixing, 2014. "Multi-index regression models with missing covariates at random," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 123(C), pages 345-363.
  2. Lai, Peng & Wang, Qihua & Lian, Heng, 2012. "Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 105(1), pages 422-432.
  3. Huang, Zhensheng & Zhang, Riquan, 2011. "Efficient empirical-likelihood-based inferences for the single-index model," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 102(5), pages 937-947, May.

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