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Semiparametric efficient estimation for partially linear single-index models with responses missing at random

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  • Lai, Peng
  • Wang, Qihua

Abstract

In this paper, we establish the semiparametric efficient bound for the heteroscedastic partially linear single-index model with responses missing at random, and develop an efficient estimating equation method. By solving the estimating equation, we obtain estimators for the parameter vectors in the linear part and the single index part simultaneously. The estimators are asymptotically semiparametrically efficient when the propensity score function is specified correctly. It should be noted that the inverse probability weighted efficient estimating equation cannot be obtained directly from the full data efficient estimating equation by the inverse probability weighted approach. We establish the estimating equation by deriving the observed data efficient score function. Some simulation studies and a real data application were conducted to evaluate and illustrate the proposed methods.

Suggested Citation

  • Lai, Peng & Wang, Qihua, 2014. "Semiparametric efficient estimation for partially linear single-index models with responses missing at random," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 33-50.
    • Handle: RePEc:eee:jmvana:v:128:y:2014:i:c:p:33-50
    DOI: 10.1016/j.jmva.2014.03.001
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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    3. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    4. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
    5. Liang H. & Wang S. & Robins J.M. & Carroll R.J., 2004. "Estimation in Partially Linear Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 357-367, January.
    6. 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.
    7. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    8. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    9. Yanyuan Ma & Liping Zhu, 2013. "Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 305-322, March.
    10. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    11. Qin, Jing & Shao, Jun & Zhang, Biao, 2008. "Efficient and Doubly Robust Imputation for Covariate-Dependent Missing Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 797-810, June.
    12. 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.
    13. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, vol. 93(1), pages 75-84, March.
    14. Z. Tan, 2011. "Efficient restricted estimators for conditional mean models with missing data," Biometrika, Biometrika Trust, vol. 98(3), pages 663-684.
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    Cited by:

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    2. Fangfang Li & Hui Sun & Yu Gu & Ge Yu, 2022. "A Noise-Aware Multiple Imputation Algorithm for Missing Data," Mathematics, MDPI, vol. 11(1), pages 1-16, December.
    3. Wei, Yuting & Wang, Qihua, 2021. "Cross-validation-based model averaging in linear models with response missing at random," Statistics & Probability Letters, Elsevier, vol. 171(C).
    4. Luo, Wei & Cai, Xizhen, 2016. "A new estimator for efficient dimension reduction in regression," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 236-249.
    5. Lai, Peng & Zhang, Qingzhao & Lian, Heng & Wang, Qihua, 2016. "Efficient estimation for the heteroscedastic single-index varying coefficient models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 84-93.

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