• 论文 •

### 协变量有测量误差时Tobit回归模型的估计

1. 1. 北 京工业大学理学部, 北京 100124; 2.中国科学院大学数学科学学院,北京 100049;3. 中国 科学院大数据挖掘与知识管理重点实验室,北京 100049
• 出版日期:2020-09-25 发布日期:2020-11-16

NIU Juan, XIE Tianfa, GUO Yuanyuan,SUN Zhihua. Estimation of Tobit Regression Model When Covariates Are Measured With Errors[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(9): 1672-1686.

### Estimation of Tobit Regression Model When Covariates Are Measured With Errors

NIU Juan1 ,XIE Tianfa1 ,GUO Yuanyuan2 ,SUN Zhihua 2,3

1. 1.Faculty of Science, Beijing University of Technology, Beijing 100124; 2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049; 3. Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100049
• Online:2020-09-25 Published:2020-11-16

In this paper, we mainly consider the estimation of the Tobit model when the covariates are measured with the errors. It is unnecessary to assume the structure of the measurement error model or the known error variance for the proposed method. At the same time, the repeated measurements data are not required. With the help of the auxiliary variable, an estimator of the true variable can be obtained by applying the local smoothing method. The true variables are replaced by their estimators and then an estimator of the regression coefficient can be defined via minimizing the corrected least squares objective function. An algorithm is presented to compute the proposed estimator and the asymptotic normality of the proposed estimator is acquired. The numerical simulation studies are conducted, which show that the proposed method performs better than the naive method. The proposed method is employed to analyze a revised real data of Duchenne Muscular Dystrophy.

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