Suboptimal robust estimation using rank score functions

A parameter estimation scheme based on the adaptive modelling of the score function of M-estimators is presented. The weights of basis functions are estimated from the data to match the empirical distribution. The bases utilise rank based score functions to remove dependence on scale from the basis selection process. While determination of appropriate bases for a distribution is shown to be possible, the robustness and adaptivity of the scheme means good results may be achieved regardless.