In survival analysis, the accelerated failure time model is a useful alternative to the popular Cox proportional hazards model due to its easy interpretation. Current estimation methods for the accelerated failure time model mostly assume independent and identically distributed random errors, but in many applications the conditional variance of log survival times depend on covariates exhibiting some form of heteroscedasticity. In this paper, we develop a local Buckley-James estimator for the accelerated failure time model with heteroscedastic errors. We establish the consistency and asymptotic normality of the proposed estimator and propose a resampling approach for inference. Simulations demonstrate that the proposed method is flexible and leads to more efficient estimation when heteroscedasticity is present. The value of the proposed method is further assessed by the analysis of a breast cancer data set.
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