A mixed integer programming approach for accommodating outliers with the minimax absolute error criterion

Minimax absolute error (MMAE) is a data fitting criterion which has several desirable features. However at the same time, this criterion is especially sensitive to the influence of outliers. In this paper the authors discuss a minimax problem which can be solved by a mixed integer programming model, which is paired with the MMAE criterion to provide simultaneous determination of candidate outliers along with model parameter estimation. They limit discussion to the case of one dependent variable per observation and focus attention on data fitting rather than inferential issues.