Robust cluster-based multivariate outlier diagnostics and parameter estimation in regression analysis

A robust regression method with substantial efficiency, high breakdown regression, and providing description of likely outlier structure is introduced. The proposed method is an agglomeration of procedures beginning from the use of Minimum Mahalanobis Distance (MMD) in constructing a cluster phase to a bounded influence regression phase. Cluster analysis partitions the data into one main cluster of half-set and the remaining data into one or more minor clusters. A bounded influence regression is then used to activate the minor clusters through a DFFITS-statistic. The resulting estimator is regression, scale, and affine equivariant. Simulation experiment shows the advantage of the proposed method over other robust regression techniques.