Robustifying Model Fitting

A robust method for fitting a model from a parametric family is fundamental to effective statistical analysis. A procedure is given for robustifying any model fitting process by using weights from the family from which the model is to be chosen. The weighting reduces the influence of information that is not compatible with the model family, while maintaining the basic structure of a familiar model fitting process. The procedure produces a parametric family of model fitting functions. The value of the parameter determines the degree to which the weighting influences the robustified model fit. A mechanism for determining an appropriate value for the parameter is described.