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 propose...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.展开更多
基金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.
文摘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.
