Robust fitting of mixtures using the trimmed likelihood estimator

The Maximum Likelihood Estimator (MLE) has commonly been used to estimate the unknown parameters in the finite mixture of distributions via the expectationmaximization (EM) algorithm. However, the MLE can be very sensitive to outliers in the data. Various approaches that have incorporated robustness in fitting mixtures and clustering are discussed. Special attention is given to the Weighted Trimmed Likelihood Estimator of Vandev and Neykov (1998) to estimate mixtures in a robust way. The superiority of this approach in comparison with the MLE is illustrated by examples and simulation studies.