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An Extended Single Index Model with Missing Response at Random

Author

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  • Qihua Wang
  • Tao Zhang
  • Wolfgang Karl Härdle

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 pro- posed estimators.

Suggested Citation

  • Qihua Wang & Tao Zhang & Wolfgang Karl Härdle, 2014. "An Extended Single Index Model with Missing Response at Random," SFB 649 Discussion Papers SFB649DP2014-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2014-003
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2014-003.pdf
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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.
    3. Zonghui Hu & Dean A. Follmann & Jing Qin, 2010. "Semiparametric dimension reduction estimation for mean response with missing data," Biometrika, Biometrika Trust, vol. 97(2), pages 305-319.
    4. Chang, Ziqing & Xue, Liugen & Zhu, Lixing, 2010. "On an asymptotically more efficient estimation of the single-index model," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1898-1901, September.
    5. Liping Zhu & Jinhong You & Qunfang Xu, 2014. "Statistical Inference for Single-index Panel Data Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 830-843, September.
    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. Ding, Xiaobo & Wang, Qihua, 2011. "Fusion-Refinement Procedure for Dimension Reduction With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1193-1207.
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    1. repec:oup:biomet:v:104:y:2017:i:3:p:735-742. is not listed on IDEAS

    More about this item

    Keywords

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

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