删失数据回归误差项的非参数密度估计的一致相合性(英文)

回归误差项是不可观测的. 由于回归误差项的密度函数在实际中有许多应用, 故使用非参数方法对其进行估计就成为回归分析中的一个基本问题. 针对完全观测数据回归模型, 曾有作者对此问题进行了研究. 然而在实际应用中, 经常会有数据被删失的情况发生, 在此情况下, 可以利用删失回归残差, 并使用核估计的方法对回归误差项的密度函数进行估计. 本文研究了该估计的大样本性质, 并证明了估计量的一致相合性.

Uniform Consistency of the Nonparametric Error Density Estimation in Regression with Censored Data

Nonparametric estimation of the density function of unobservable regression errors is a fundamental issue in regression analysis, because there are many practical applications of error density estimation. This problem for regression models with complete observed data has been studied by several authors. But in many application fields, the corresponding variables are not complete observable because of censoring. In this case, the density function of the unobservable regression errors can be estimated by the kernel type estimator based on the censored regression residuals.In this paper, the asymptotic property of the kernel type estimator is considered and the uniform consistency of the estimator is established.