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M-estimators for single-index model using B-spline

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  • Qingming Zou
  • Zhongyi Zhu

Abstract

The single-index model is an important tool in multivariate nonparametric regression. This paper deals with M-estimators for the single-index model. Unlike the existing M-estimator for the single-index model, the unknown link function is approximated by B-spline and M-estimators for the parameter and the nonparametric component are obtained in one step. The proposed M-estimator of unknown function is shown to attain the convergence rate as that of the optimal global rate of convergence of estimators for nonparametric regression according to Stone (Ann Stat 8:1348–1360, 1980 ; Ann Stat 10:1040–1053, 1982 ), and the M-estimator of parameter is $$\sqrt{n}$$ -consistent and asymptotically normal. A small sample simulation study showed that the M-estimators proposed in this paper are robust. An application to real data illustrates the estimator’s usefulness. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Qingming Zou & Zhongyi Zhu, 2014. "M-estimators for single-index model using B-spline," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 225-246, February.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:2:p:225-246
    DOI: 10.1007/s00184-013-0434-z
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    2. Han, Jinyue & Wang, Jun & Gao, Wei & Tang, Man-Lai, 2023. "Estimation of the directions for unknown parameters in semiparametric models," MPRA Paper 116365, University Library of Munich, Germany.

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