Research article

Multiple robust estimation of parameters in varying-coefficient partially linear model with response missing at random

  • Received: 25 December 2021 Revised: 06 February 2022 Accepted: 10 February 2022 Published: 08 March 2022
  • In this paper, we consider the multiple robust estimation of the parameters in the varying-coefficient partially linear model with response missing at random. The multiple robust estimation method is proposed, and the multiple robustness of the proposed method is proved. Numerical simulations are conducted to investigate the finite sample performance of the proposed estimators compared with other competitors.

    Citation: Yaxin Zhao, Xiuli Wang. Multiple robust estimation of parameters in varying-coefficient partially linear model with response missing at random[J]. Mathematical Modelling and Control, 2022, 2(1): 24-33. doi: 10.3934/mmc.2022004

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  • In this paper, we consider the multiple robust estimation of the parameters in the varying-coefficient partially linear model with response missing at random. The multiple robust estimation method is proposed, and the multiple robustness of the proposed method is proved. Numerical simulations are conducted to investigate the finite sample performance of the proposed estimators compared with other competitors.



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    [1] J. Fan, T. Huang, Profile Likelihood Inferences on Semiparametric Varying-Coefficient Partially Linear Models, Bernoulli, 11 (2005), 1031–1057. https://doi.org/10.3150/bj/1137421639 doi: 10.3150/bj/1137421639
    [2] J. You, Y. Zhou, Empirical likelihood for semiparametric varying-coefficient partially linear regression models, Stat. Probabil. Lett., 76 (2006), 412–422. https://doi.org/10.1016/j.spl.2005.08.029 doi: 10.1016/j.spl.2005.08.029
    [3] Z. Huang, R. Zhang, Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models, Stat. Probabil. Lett., 79 (2009), 1798–1808. https://doi.org/10.1016/j.spl.2009.05.008 doi: 10.1016/j.spl.2009.05.008
    [4] P. Zhao, Infrerence for semiparametric varying coefficient partially linear models, doctoral dissertation, Beijing: Beijing University of Technology, 2010.
    [5] J. Feng, R. Zhang, Y. Lu, Inference on varying-coefficient partially linear regression model, Acta Math. Appl. Sin-E, 31 (2015), 139–156. https://doi.org/10.1007/s10255-015-0457-5 doi: 10.1007/s10255-015-0457-5
    [6] R. Little, D. Rubin, Statistical analysis with missing data, 1 Eds., New York: Wiley Press, 1986.
    [7] D. Horvitz, D. Thompson, A generalization of sampling without replacement from a finite universe, J. Am. Stat. Assoc., 47 (1952), 663–685. https://doi.org/10.1080/01621459.1952.10483446 doi: 10.1080/01621459.1952.10483446
    [8] F. Yates, The analysis of replicated experiments when the field results are incomplete, Exp. Agr., 1 (1933), 129–142.
    [9] P. Cheng, Nonparametric estimation of mean functionals with data missing at random, J. Am. Stat. Assoc., 89 (1994), 81–87. https://doi.org/10.1080/01621459.1994.10476448 doi: 10.1080/01621459.1994.10476448
    [10] Q. Wang, J. Rao, Empirical likelihood for linear regression models under imputation for missing responses, Can. J. Stat., 29 (2001), 596–608. https://doi.org/10.2307/3316009 doi: 10.2307/3316009
    [11] Q. Wang, J. Rao, Empirical likelihood-based inference under imputation for missing response data, Ann. Stat., 30 (2002), 896–924. https://doi.org/10.1214/aos/1028674845 doi: 10.1214/aos/1028674845
    [12] Q. Wang, O. Linton, W. Hardle, Semi-parametric regression analysis with missing response at random, J. Am. Stat. Assoc., 99 (2004), 334–345. https://doi.org/10.1198/016214504000000449 doi: 10.1198/016214504000000449
    [13] J. Robins, A. Rotnitzky, L. Zhao, Estimation of Regression Coefficients When Some Regressors Are Not Always Observed, J. Am. Stat. Assoc., 89 (1994), 846–866. https://doi.org/10.1080/01621459.1994.10476818 doi: 10.1080/01621459.1994.10476818
    [14] J. Robins, A. Rotnitzky, Semiparametric efficiency in multivariate regression models with missing data, J. Am. Stat. Assoc., 90 (1995), 122–129. https://doi.org/10.1080/01621459.1995.10476494 doi: 10.1080/01621459.1995.10476494
    [15] D. Scharfstein, A. Rotnitzky, R. Robins, Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models, J. Am. Stat. Assoc., 94 (1999), 1096–1120. https://doi.org/10.1080/01621459.1999.10473862 doi: 10.1080/01621459.1999.10473862
    [16] J. Kang, J. Schafer, Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data (with Discussion), Statistics, 22 (2007), 523–539. https://doi.org/10.1214/07-STS227 doi: 10.1214/07-STS227
    [17] J. Qin, J. Shao, B. Zhang, Efficient and doubly robust imputation for covariate-dependent missing responses, J. Am. Stat. Assoc., 103 (2008), 797–810. https://doi.org/10.1198/016214508000000238 doi: 10.1198/016214508000000238
    [18] W. Cao, A. Tsiatis, M. Davidian, Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data, Biometrika, 96 (2009), 723–734. https://doi.org/10.1093/biomet/asp033 doi: 10.1093/biomet/asp033
    [19] P. Han, A note on improving the efficiency of inverse probability weighted estimator using the augmentation term, Stat. Probabil. Lett., 82 (2012), 2221–2228. https://doi.org/10.1016/j.spl.2012.08.005 doi: 10.1016/j.spl.2012.08.005
    [20] A. Rotnitzky, Q. Lei, M. Sued, J. Robins, Improved double-robust estimation in missing data and causal inference models, Biometrika, 99 (2012), 439–456. https://doi.org/10.1093/biomet/ass013 doi: 10.1093/biomet/ass013
    [21] P. Han, L. Wang, Estimation with missing data: Beyond double robustness, Biometrika, 100 (2013), 417–430. https://doi.org/10.1093/biomet/ass087 doi: 10.1093/biomet/ass087
    [22] P. Han, Multiply Robust Estimation in Regression Analysis With Missing Data, J. Am. Stat. Assoc., 109 (2014), 1159–1173. https://doi.org/10.1080/01621459.2014.880058 doi: 10.1080/01621459.2014.880058
    [23] Y. Sun, L. Wang, P. Han, Multiply robust estimation in nonparametric regression with missing data, J. Nonparametr. Stat., 32 (2020), 73–92. https://doi.org/10.1080/10485252.2019.1700254 doi: 10.1080/10485252.2019.1700254
    [24] P. Han, Calibration and multiple robustness when data are missing not at random, Stat. Sinica, 109 (2018), 1725–1740. https://doi.org/10.5705/ss.202015.0408 doi: 10.5705/ss.202015.0408
    [25] W. Li, S. Yang, P. Han, Robust estimation for moment condition models with data missing not at random, J. Stat. Plan. Infer., 207 (2020), 246–254. https://doi.org/10.1016/j.jspi.2020.01.001 doi: 10.1016/j.jspi.2020.01.001
    [26] H. White, Maximum likelihood estimation of misspecified models, Econometrica, 50 (1982), 1–25. https://doi.org/10.2307/1912526 doi: 10.2307/1912526
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