Performance of the Bartlett and Bartlett-type corrections in some location-scale nonlinear models

Statistical inference based on the normal model is known to be vulnerable to outliers. Despite this fact and the considerable interest in robust procedures in the statistical literature, most applied statistical analysis continues to be based on the normal model. Our approach is to replace the normal model by a general location-scale family of nonlinear models which include several asymmetric distributions that have a wide range of practical applications for analysing univariate data. We focus on the second-order corrections to the likelihood ratio and score statistics, since they are the most commonly used large sample tests. We obtain simple formulae for the corrections in some special location-scale models. We use Monte Carlo simulation to show that the corrected likelihood ratio and score tests have empirical sizes closer to the nominal sizes than the classical uncorrected tests even when the scale parameter in replaced by a consistent estimate.