Signed-rank regression inference via empirical likelihood

Abstract

For the general stochastic regression analysis of complete data, Bindele and Abebe [Bounded influence nonlinear signed-rank regression. Can J Stat. 2012;40(1):172–189. Available from: http://dx.doi.org/10.1002/cjs.10134 ] proposed the signed-rank (SR) estimator. However, there exists an over-coverage problem for the confidence intervals of the regression parameters when the sample size is small. In this paper, we investigate an empirical likelihood (EL) approach to construct confidence intervals for the regression parameters based on the SR estimating equation. The limiting distribution of log-empirical likelihood ratio is χ2 distribution. We carry out extensive simulation studies to compare the proposed method with the normal approximation-based method. The simulation results show that the proposed method outperforms the existing method in terms of the coverage probability and average length of confidence intervals. We illustrate the EL method using a real data example.