Abstract
A partial linear model with missing response variables and error-prone covariates is considered. The imputation approach is developed to estimate the regression coefficients and the nonparametric function. The proposed parametric estimators are shown to be asymptotically normal, and the estimators for the nonparametric part are proved to converge at an optimal rate. To construct confidence regions for the regression coefficients and the nonparametric function, respectively, the authors also propose the empirical-likelihood-based statistics and investigate the limit distributions of the empirical likelihood ratios. The simulation study is conducted to compare the finite sample behavior for the proposed estimators. An application to an AIDS dataset is illustrated.
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This research is supported by the National Social Science Foundation of China under Grant No. 11CTJ004, the National Natural Science Foundation of China under Grant Nos. 10871013 and 10871217, the National Natural Science Foundation of Beijing under Grant No. 1102008, the Research Foundation of Chongqing Municipal Education Commission under Grant Nos. KJ110720 and KJ100726, and the Natural Science Foundation of Guangxi under Grant No. 2010GXNSFB013051.
This paper was recommended for publication by Editor Guohua ZOU.
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Yang, Y., Xue, L. & Cheng, W. Two-step estimators in partial linear models with missing response variables and error-prone covariates. J Syst Sci Complex 24, 1165–1182 (2011). https://doi.org/10.1007/s11424-011-8393-9
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DOI: https://doi.org/10.1007/s11424-011-8393-9