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

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

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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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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  1. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
  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. 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.
  4. Peter Hall & Qiwei Yao, 2005. "Approximating conditional distribution functions using dimension reduction," LSE Research Online Documents on Economics 16333, London School of Economics and Political Science, LSE Library.
  5. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
  6. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
  7. 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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