文章考虑协变量有测量误差时参数\,Tobit\,模型的估计问题.文章所提方法 不需要假定测量误差模型的结构, 不需要对测量误差变量的方差做假定, 也不需要有重复 观测的数据. 测量误差的矫正通过借助工具变量来实现. 首先利用非参数核光滑方法得到真 实观测变量的估计, 然后用这个估计替代没有观察到的真实变量来处理测量误差. 这样, 模型的回归系数就可以利用校正的最小二乘方法来估计. 文章给出了具体的算法, 证明了 回归模型的参数估计的渐近正态性. 数值模拟结果表明文章提出的校正测量误差的方法比直 接使用有测量误差数据的朴素方法有更好的有限样本性质.

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.