High-order asymptotic expansions for robust tests

This paper provides high-order asymptotic expansions for the M-ratio and th e signed-root M-ratio robust test statistics, which allow one to compute ac curate approximations to significance or critical values using the Edgewort h approximation, the Bartlett correction, the variance correction or the sa ddlepoint approximation. Specific results are obtained for the linear regre ssion model with the Huber M-estimator. A Monte Carlo study illustrates the numerical accuracy of these approximations, with respect to the usual firs t-order approximations.