Citation: | GUO Donglin, XUE Liugen, HU Yuqin. Robust Estimation of Mean in Partially Linear Model With Missing Responses[J]. Journal of Beijing University of Technology, 2017, 43(2): 313-319. DOI: 10.11936/bjutxb2016040017 |
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.
[1] |
ENGLE RF, 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 JT,SHI PD.M-type smoothing splines inonparametric and semiparametric regression models[J].Statistica Sinica,1997,7(4):1155-1169.
|
[3] |
HAMILTON SA,TRUONG YK.Local linear estimation in partly linear models[J].Journal of Multivariate Analysis,1997,60(1):1-19.
|
[4] |
ROBINSON PM.Root-n-consistent semiparametric regression[J].Econometrika,1988,56(4):931-954.
|
[5] |
XUE LG,ZHU LX.Empirical likelihood-based inference in a partially linear model for longitudinal data[J].Science in China: Series A,2008,51(1):115-130.
|
[6] |
QINJ,SHAOJ,ZHANGB.Efficient and doubly robust imputation for covariate-dependent missing responses[J].Journal of the American Statistical Association,2008,103(482):797-810.
|
[7] |
QINJ,ZHANGB.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 JM,ROTNITZKYA.Estimation of regression coefficients when some regressors are not always observed[J].Journal of the American Statistical Association,1994,89(427):846-866.
|
[9] |
WANGD,CHEN SX.Empirical likelihood for estimating equations with missing values[J].The Annals of Statistics,2009,37(1):490-517.
|
[10] |
ZHOUY,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] |
WANGQ,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 LG.Empirical likelihood for linear models with missing responses[J].Journal of Multivariate Analysis,2009,100(7):1353-1366.
|
[13] |
WANG CY,WANG SJ,GUTIERREZ RG,et al.Local linear regression for generalized linear models with missing data[J].The Annals of Statistics,1998,26(3):1028-1050.
|
[14] |
XUED,XUE LG,CHENG WH.Empirical likelihood for generalized linear models with missing responses[J].Journal of Statistical Planning and Inference,2011,141(6):2007-2020.
|
[15] |
ZHAO PX,XUE LG.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] |
LIANGH,WANG SJ,ROBINS JM,et al.Estimation in partially linear models with missing covariates[J].Journal of the American Statistical Association,2004,99(466):357-367.
|
[17] |
WANG QH,LINTONO,HARDLEW.Semiparametric regression analysis with missing response at random[J].Journal of the American Statistical Association,2004 ,99(466):334-345.
|
[18] |
WANG QH,SUN ZH.Estimation in partially linear models with missing responses at random[J].Journal of Multivariate Analysis,2007,98(7):1470-1493.
|
[19] |
LIANGH,WANG SJ,ROBINS JM,et al.Partially linear models with missing response variables and error-prone covariates[J].Biometrika,2007,94(1):185-198.
|
[20] |
WANG QH.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 LG,XUED.Empirical likelihood for semiparametric regression model with missing response data[J].Journal of Multivariate Analysis,2011,102(4):723-740.
|
[22] |
LIANGH,QIN YS.Empirical likelihood-based inferencesfor partially linear models with missing covariates[J].Australian & New Zealand Journal of Statistics,2008,50(4):347-359.
|
[23] |
CAO WH,TSIATIS AA,DAVIDIANM.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 PS,WANGL.Estimation with missing data: beyond double robustness[J].Biometrika,2013,100(2):417-430.
|
[25] |
HAN PS.Multiply robust estimation in regression analysis with missing data[J].Journal of the American Statistical Association,2014,109(507),1159-1173.
|
[26] |
KANG J DY,SCHAFER JL.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] |
IMAIK,RATKOVICM.Covariate balancing propensity score[J].Journal of the Royal Statistical Society: Series B,2014,76(1):243-263.
|
[28] |
RUBIN DB.Inference and missing data[J].Biometrika,1976,63(3):581-592.
|
[29] |
HANSEN LP.Large sample properties of generalized method of moments estimators[J].Econometrica,1982,50(4):1029-1054.
|
[30] |
NEWEY WK,MCFADDEND.Large sample estimation and hypothesis testing[M].New York: Springer,1994:18-58.
|
[31] |
LIANGH.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.
|
[1] | DOU Huijing, GAO Lijing, ZHU Ziyun. DOA Estimation Based on Weighted l1 Norm Sparse Signal Representation[J]. Journal of Beijing University of Technology, 2018, 44(10): 1297-1302. DOI: 10.11936/bjutxb2017060005 |
[2] | XIN Le, REN Jianqiang, CHEN Yangzhou, HU Jiangbi, YANG Minghao. Robust Vehicle Detection and Estimation of the Lane-by-Lane Arrival Cumulative Curves for Traffic Congestion[J]. Journal of Beijing University of Technology, 2017, 43(8): 1234-1244. DOI: 10.11936/bjutxb2016080029 |
[3] | WEI Ying-zi, LIU Xiao-li. Robust Plane Fitting of Point Clouds Based on RANSAC[J]. Journal of Beijing University of Technology, 2014, 40(3): 400-403. DOI: 10.3969/j.issn.0254-0037.2014.03.014 |
[4] | WANG Jin-ru, WANG Meng. Linear Wavelet Density Estimation for Biased Data[J]. Journal of Beijing University of Technology, 2013, 39(11): 1752-1755. DOI: 10.3969/j.issn.0254-0037.2013.11.025 |
[5] | ZHAO Xu, XUE Liu-gen, LI Jing-lan, CHENG Wei-hu. Parameter Estimation of Approximated Generalized Least Squares Estimators for the Generalized Pareto Distribution[J]. Journal of Beijing University of Technology, 2012, 38(5): 789-792. DOI: 10.3969/j.issn.0254-0037.2012.05.029 |
[6] | ZHAO Pei-xin, XUE Liu-gen. Robust Estimation for Varying Coefficient Model[J]. Journal of Beijing University of Technology, 2011, 37(2): 302-305,313. DOI: 10.3969/j.issn.0254-0037.2011.02.024 |
[7] | LI Zhi-qiang, XUE Liu-gen. The Generalized Semiparametric Models with Missing Covariates[J]. Journal of Beijing University of Technology, 2007, 33(7): 761-765. DOI: 10.3969/j.issn.0254-0037.2007.07.018 |
[8] | CHEN Nai-hui. Optimality of Generalized Interval Estimating of Derived Parameters Under Two Totals[J]. Journal of Beijing University of Technology, 2006, 32(3): 274-277,288. DOI: 10.3969/j.issn.0254-0037.2006.03.016 |
[9] | Tan Liyang, Weber T W. Robustness of A Biased Estimator with Easily-Tuned Parameters[J]. Journal of Beijing University of Technology, 1994, 20(1): 31-36. |
[10] | Ding Ping, Zhou Zheng, Zhou Ming-fang. An Improvement to Borwein's Precise Estimate[J]. Journal of Beijing University of Technology, 1986, 12(4): 91-95. |