Empirical likelihood with twice censored data

We consider the problem of the construction of confidence intervals for some functionals of a distribution of interest. These functionals include the moments of the distribution, the survival function, and the mean residual life, among others. The empirical likelihood method has been extensively used to construct such confidence intervals in the cases of complete and right censored data. In this article, we deal with the case of twice censored data, where right and left censoring are simultaneously involved. In this context, we propose an empirical likelihood ratio function which we use to construct confidence intervals for some functionals of the distribution of interest. The advantage of our method lies in the fact that our proposed empirical likelihood ratio function converges to a chi-square distribution without being multiplied by any scale parameters, which is the case for many empirical likelihood versions that exist in the setting of censored data. Therefore, we use our empirical likelihood ratio function to construct the desired confidence intervals without involving any further estimation of the scale parameters. This allows to improve the coverage accuracy of our confidence intervals. Finally, we show the performances of our method through a simulation study and a real data application.