Empirical likelihood inference for rank regression with doubly truncated data

Abstract

For regression analysis of doubly truncated data, we propose two empirical likelihood (EL) inference approaches, called non-smooth EL and non-smooth Jackknife EL (JEL), to make inference about regression parameters based on the generalized estimating equations of existing weighted rank estimators. The limiting distributions of non-smooth log-EL and log-JEL ratios statistics are derived and non-smooth EL, and JEL confidence intervals for any specified component of regression parameters are obtained. We carry out extensive simulation studies to compare the proposed approaches with the random weighting (RW) approach. The simulation results demonstrate that the non-smooth EL and JEL confidence intervals have better performances than the RW confidence intervals based on coverage probability and average length of confidence intervals of regression parameters when the dependent variable is subject to the double truncation. A real data example is provided to illustrate the proposed approaches.