Robust fitting of mixtures using the trimmed likelihood estimator

The maximum likelihood estimator (MLE) has commonly been used to estimate the unknown parameters in a finite mixture of distributions. However, the MLE can be very sensitive to outliers in the data. In order to overcome this the trimmed likelihood estimator (TLE) is proposed to estimate mixtures in a robust way. The superiority of this approach in comparison with the MLE is illustrated by examples and simulation studies. Moreover, as a prominent measure of robustness, the breakdown point (BDP) of the TLE for the mixture component parameters is characterized. The relationship of the TLE with various other approaches that have incorporated robustness in fitting mixtures and clustering are also discussed in this context.