Ranks

Rank tests were introduced as a reaction against the traditional assumption of Gaussian observations. The most attractive feature of ranks and rank statistics is that they are distribution-free, and thus, in principle, allow for exact critical values, irrespective of the underlying distribution of the observation. Their domain of application is, mainly but not exclusively, the class of semiparametric models obtained from the traditional parametric ones (location, scale, regression, autoregression, etc.) by treating the density of the underlying error or noise as an unspecified nuisance. Their popularity is explained by their success in a variety of practical situations, and their robustness against deviations from standard distributional assumptions.