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