Smoothed empirical likelihood confidence intervals for the relative distribution with left truncated and right censored data

摘要

The study of differences among groups is an interesting statistical topic in many applied fields. It is very common in this context to have data that are sub ject to mechanisms of loss of information, such as censoring and truncation. In the setting of a two-sample problem with data sub ject to left truncation and right censoring, we develop an empirical likelihood method to do inference for the relative distribution. We obtain a nonparametric generalization of Wilks’ theorem and construct nonparametric pointwise confidence intervals for the relative distribution. Finally, we analyze the coverage probability of these confidence intervals through a simulation study.