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

Qingming Zou and Zhongyi Zhu ()

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 2, 225-246

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

Keywords: B-spline; M-estimator; Rate of convergence; Single-index model (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00184-013-0434-z

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