The rtclust procedure for robust clustering

new robust model based clustering method is proposed, which is based on trimming and reweighting. In parallel with the case of location and scatter estimation, reweighting allows to achieve high breakdown together with high efficiency. Additionally, the user does not need to set the trimming level in advance. The method proceeds by fitting an initial robust finite mixture model based on a high trimming level. Observations with high robust Mahalanobis distance from the closest centroid are then flagged as outlying, and centroid estimation is repeated based on the other ones. The procedure is iterated until convergence. It is shown formally, with examples, and with extensive simulation studies that the resulting rtclust procedure can resist to different outlier generating schemes, and is highly efficient in the presence of little or no contamination. Additionally, the new procedure compares well and does not need much tuning.