Empirical likelihood inference for median regression models for censored survival data

Recent advances in median regression model have made it possible to use this model for analyzing a variety of censored survival data. For inference on the model parameter vector, there are now semiparametric procedures based on normal approximation that are valid without strong conditions on the error distribution. However, the accuracy of such procedures can be quite low when the censoring proportion is high. In this paper, we propose an alternative semiparametric procedure based on the empirical likelihood. We define the empirical likelihood ratio for the parameter vector and show that its limiting distribution is a weighted sum of chi-square distributions. Numerical results from a simulation study suggest that the empirical likelihood method is more accurate than the normal approximation based method of Ying et al. (J. Amer. Statist. Assoc. 90 (1995) 178).