In the field of rotor balancing, the traditional influence coefficient method is often employed along with weighted least squares in order to reduce amplitude vibrations, typically at selected rotating speeds such as critical or operating ones. Usually, these weights are manually selected by the operator. In this paper, an automatic procedure for the balancing mass estimation based on robust regression methods is introduced. The analysis is focused on high breakdown-point and bounded-influence estimators. The effectiveness and robustness of the proposed balancing procedure are shown by means of simulations of a 180 MW gas turbo generator of a power plant.