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An extended single index model with missing response at random

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  • Wang, Qihua
  • Zhang, Tao
  • Härdle, Wolfgang Karl

Abstract

An extended single-index model is considered when responses are missing at random. A three-step estimation procedure is developed to define an estimator for the single index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation study is conducted to investigate the finite sample performances of the proposed estimators.

Suggested Citation

  • Wang, Qihua & Zhang, Tao & Härdle, Wolfgang Karl, 2014. "An extended single index model with missing response at random," SFB 649 Discussion Papers 2014-003, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2014-003
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    References listed on IDEAS

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    1. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    2. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
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    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.
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    Cited by:

    1. Ash Abebe & Huybrechts F. Bindele & Masego Otlaadisa & Boikanyo Makubate, 2021. "Robust estimation of single index models with responses missing at random," Statistical Papers, Springer, vol. 62(5), pages 2195-2225, October.
    2. Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.
    3. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    4. Wei Luo, 2022. "On efficient dimension reduction with respect to the interaction between two response variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 269-294, April.

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    Keywords

    Missing data; Estimating equations; Single-index models; Asymptotic normality;
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