Asymptotic expansions and the reliability of tests in accelerated failure time models

This paper gives matrix formulae for the O(n(-1)) correction applicable to asymptotically efficient conditional moment tests. These formulae only require expectations of functions involving, at most, second order derivatives of the log-likelihood; unlike those previously provided by Ferrari and Cordeiro (1994). The correction is used to assess the reliability of first order asymptotic theory for arbitrary residual-based diagnostics in a class of accelerated failure time models: this correction is always parameter free, depending only on the number of included covariates in the regression design. For all but one of the tests considered, first order theory is found to be extremely unreliable, even in quite large samples, although this may not be widely appreciated by applied workers.