Maximum likelihood robust regression by mixture models

In this paper, we will consider a robust estimator, which was proposed earlier by the authors, in a general non-linear regression framework. The basic idea of the estimator is, instead of trying to classify the observations to good and false, to model the residual distribution of the contaminants, determine the probability for each observation to be a good sample, and finally perform weighted fitting. The main contributions of this paper are: (1) We show now that the estimator is consistent with the true parameter values that simply means optimality regardless of the problematical outliers in the observations. (2) We propose how robust uncertainty computations and robust model selection can be performed in the similar, consistent manner. (3) We derive the expectation maximisation algorithm for the estimator and (4) extend the estimator to handle unknown outlier residual distributions. (5) We finally give some experiments with real data, where robustness in model fitting is needed.