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Weighted estimation of single index models with right censored responses

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Abstract

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

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Authors and Affiliations

  1. School of Sciences, Beijing Institute of Technology, Beijing, 100081, China

    YanHua Wang

  2. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    XiaYan Li

  3. Chinese Academy of Mathematics and System Science, Beijing, 100080, China

    QiHua Wang

  4. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    ShuYuan He

Authors
  1. YanHua Wang
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  2. XiaYan Li
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  3. QiHua Wang
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  4. ShuYuan He
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Correspondence to YanHua Wang.

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Wang, Y., Li, X., Wang, Q. et al. Weighted estimation of single index models with right censored responses. Sci. China Math. 54, 479–514 (2011). https://doi.org/10.1007/s11425-010-4155-8

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  • DOI: https://doi.org/10.1007/s11425-010-4155-8

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