Accelerated Failure Time Models with Logconcave Errors

We study accelerated failure time models in which the survivor function of the error term is log-concave. The log-concavity assumption is often implied by the underlying economic models and covers large families of commonly used distributions. For right-censored failure time data, we construct semi-parametric maximum likelihood estimates of the finite dimensional parameter subject to the shape restriction and establish the large sample properties. The shape restriction also facilitates computation, as the optimization problem has a unique global solution with probability tending to one. Simulation studies and empirical applications demonstrate the usefulness of our method