Empirical Likelihood Analysis for the Heteroscedastic Accelerated Failure Time Model

In this manuscript, we discuss the distinction of two types of data generating scheme for the accelerated failure time model. We identify two different empirical likelihood formulations under random right censoring, case-wise and residual-wise, each reflecting the relevant features of the stochastic model assumed to have generated the data. We specifically 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.