  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 correct detection rates and low false detection
rates in the vast majority of cases, as well as the significantly smaller
computation time shows the advantages of our proposal.
