A collection of robust Mahalanobis distances for multivariate outlier detection is proposed, based on the notion of shrinkage. Robust intensity and scaling factors are optimally estimated to define the shrinkage. Some properties are investigated, such as affine equivariance and breakdown value. The performance of the proposal is illustrated through the comparison to other techniques from the literature, in a simulation study and with a real dataset. The behavior when the underlying distribution is heavy-tailed or skewed, shows the appropriateness of the method when we deviate from the common assumption of normality. The resulting high true positive rates and low false positive rates in the vast majority of cases, as well as the significantly smaller computation time show the advantages of our proposal.

A robust multivariate quality control technique for individual observations is proposed, based on the robust reweighted shrinkage estimators. A simulation study is done to check the performance and compare the method with the classical Hotelling approach, and the robust alternative based on the reweighted minimum covariance determinant estimator. The results show the appropriateness of the method even when the dimension or the Phase I contamination are high, with both independent and correlated variables, showing additional advantages about computational efficiency. The approach is illustrated with two real data-set examples from production processes.