RESEARCH ARTICLE Empirical Likelihood Analysis for the Heteroscedastic Accelerated Failure Time Model

two dierent formulations of empirical likelihood that correspond to these models. In this manuscript, we revisit this distinction for the accelerated failure time model under random right censoring. We identify two dierent empirical likelihood formulations under random right censoring, case-wise and residual-wise, each reecting the relevant features of the stochastic model assumed to have generated the data. We specically propose the case-wise empirical likelihood as a computationally simple inference method for the accelerated failure time model with heteroscedastic errors. A nonparametric version of Wilks’ theorem is shown to hold for the resulting likelihood ratio. The results are also applicable to censored quantile regression, illustrated in an example.