Volume 43 Issue 2
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JOURNAL OF MECHANICAL ENGINEERING  > 2017  >  43(2): 313-319.
GUO Donglin, XUE Liugen, HU Yuqin. Robust Estimation of Mean in Partially Linear Model With Missing Responses[J]. JOURNAL OF MECHANICAL ENGINEERING, 2017, 43(2): 313-319. doi: 10.11936/bjutxb2016040017
Citation: GUO Donglin, XUE Liugen, HU Yuqin. Robust Estimation of Mean in Partially Linear Model With Missing Responses[J]. JOURNAL OF MECHANICAL ENGINEERING, 2017, 43(2): 313-319. doi: 10.11936/bjutxb2016040017
shu

Robust Estimation of Mean in Partially Linear Model With Missing Responses

doi: 10.11936/bjutxb2016040017
  • 1.

    College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

  • 2.

    School of Mathematics and Information Science, Shangqiu Normal University, Shangqiu 476000, Henan, China

  • 3.

    School of data science, Zhejiang University of Finance and Economics, Hangzhou 310018, China

  • Received Date: 07 Apr 2016
    Available Online: 13 Sep 2022
  • Issue Publish Date: 01 Feb 2017
    Abstract
  • To improve the robustness of an estimator, based on the covariate balancing propensity score and the augmented inverse probability weighted methods, a robust estimator of the population mean was obtained for the partially linear model, when the responses were missing at random. It is proved that the proposed estimator is asymptotically normal, and hence it can be applied to constructing the confidence region of the population mean.

     

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  • [1]
    ENGLE R F, GRANGER C W J, RICE J, et al. Semiparametric estimates of the relation between weather and electricity sales[J]. Journal of the American Statistical Association, 1986, 81(394): 310-320.
    [2]
    GAO J T, SHI P D.M-type smoothing splines inonparametric and semiparametric regression models[J]. Statistica Sinica, 1997, 7(4): 1155-1169.
    [3]
    HAMILTON S A, TRUONG Y K.Local linear estimation in partly linear models[J]. Journal of Multivariate Analysis, 1997, 60(1): 1-19.
    [4]
    ROBINSON P M.Root-n-consistent semiparametric regression[J]. Econometrika, 1988, 56(4): 931-954.
    [5]
    XUE L G, ZHU L X.Empirical likelihood-based inference in a partially linear model for longitudinal data[J]. Science in China: Series A, 2008, 51(1): 115-130.
    [6]
    QIN J, SHAO J, ZHANG B.Efficient and doubly robust imputation for covariate-dependent missing responses[J]. Journal of the American Statistical Association, 2008, 103(482): 797-810.
    [7]
    QIN J, ZHANG B.Empirical-likelihood-based inference in missing response problems and its application in observational studies[J]. Journal of the Royal Statistical Society: Series B, 2007, 69(1): 101-122.
    [8]
    ROBINS J M, ROTNITZKY A.Estimation of regression coefficients when some regressors are not always observed[J]. Journal of the American Statistical Association, 1994, 89(427): 846-866.
    [9]
    WANG D, CHEN S X.Empirical likelihood for estimating equations with missing values[J]. The Annals of Statistics, 2009, 37(1): 490-517.
    [10]
    ZHOU Y, WAN A T K, WANG X J. Estimating equations inference with missing data[J]. Journal of the American Statistical Association, 2008, 103(483): 1187-1199.
    [11]
    WANG Q, RAO J N K. Empirical likelihood-based inference in linear models with missing data[J]. Scandinavian Journal of Statistics, 2002, 29(3): 563-576.
    [12]
    XUE L G.Empirical likelihood for linear models with missing responses[J]. Journal of Multivariate Analysis, 2009, 100(7): 1353-1366.
    [13]
    WANG C Y, WANG S J, GUTIERREZ R G, et al.Local linear regression for generalized linear models with missing data[J]. The Annals of Statistics, 1998, 26(3): 1028-1050.
    [14]
    XUE D, XUE L G, CHENG W H.Empirical likelihood for generalized linear models with missing responses[J]. Journal of Statistical Planning and Inference, 2011, 141(6): 2007-2020.
    [15]
    ZHAO P X, XUE L G.Variable selection for semiparametric varying-coefficient partially linear models with missing response at random[J]. Acta Methematica Sinica: English series, 2011, 27(11): 2205-2216.
    [16]
    LIANG H, WANG S J, ROBINS J M, et al.Estimation in partially linear models with missing covariates[J]. Journal of the American Statistical Association, 2004, 99(466): 357-367.
    [17]
    WANG Q H, LINTON O, HARDLE W.Semiparametric regression analysis with missing response at random[J]. Journal of the American Statistical Association, 2004 , 99(466): 334-345.
    [18]
    WANG Q H, SUN Z H.Estimation in partially linear models with missing responses at random[J]. Journal of Multivariate Analysis, 2007, 98(7): 1470-1493.
    [19]
    LIANG H, WANG S J, ROBINS J M, et al.Partially linear models with missing response variables and error-prone covariates[J]. Biometrika, 2007, 94(1): 185-198.
    [20]
    WANG Q H.Statistical estimation in partial linear models with covariate data missing at random[J]. Annals of the Institute of Statistical Mathematics, 2009, 61(1): 47-84.
    [21]
    XUE L G, XUE D.Empirical likelihood for semiparametric regression model with missing response data[J]. Journal of Multivariate Analysis, 2011, 102(4): 723-740.
    [22]
    LIANG H, QIN Y S.Empirical likelihood-based inferencesfor partially linear models with missing covariates[J]. Australian & New Zealand Journal of Statistics, 2008, 50(4): 347-359.
    [23]
    CAO W H, TSIATIS A A, DAVIDIAN M.Improving efficiency and roubustness of the doubly robust estimator for a population mean with incomplete data[J]. Biometrika, 2009, 96(3): 723-734.
    [24]
    HAN P S, WANG L.Estimation with missing data: beyond double robustness[J]. Biometrika, 2013, 100(2): 417-430.
    [25]
    HAN P S.Multiply robust estimation in regression analysis with missing data[J]. Journal of the American Statistical Association, 2014, 109(507), 1159-1173.
    [26]
    KANG J D Y, SCHAFER J L. Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data[J]. Statistical Science, 2007, 22(4): 523-539.
    [27]
    IMAI K, RATKOVIC M.Covariate balancing propensity score[J]. Journal of the Royal Statistical Society: Series B, 2014, 76(1): 243-263.
    [28]
    RUBIN D B.Inference and missing data[J]. Biometrika, 1976, 63(3): 581-592.
    [29]
    HANSEN L P.Large sample properties of generalized method of moments estimators[J]. Econometrica, 1982, 50(4): 1029-1054.
    [30]
    NEWEY W K, MCFADDEN D.Large sample estimation and hypothesis testing[M]. New York: Springer, 1994: 18-58.
    [31]
    LIANG H.Asymptotic normality of parametric part in partially linear models with measurement error in the nonparametric part[J]. Journal of Statistical Planning and Inference, 2000, 86(1): 51-62.
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