A co-median approach to detect compositional outliers

Compositional data consist of vectors of positive values summing up to a unit or to some fixed constant. They find application in chemometrics, geology, economics, psychometrics and many other field of studies. In statistical analysis many theoretical efforts have been dedicated to identify procedures able to accomodate outliers included in the estimation of the model even in compositional data. The principal purpose of this work is to introduce an alternative robust procedure, defined as COMCoDa, capable to cope with compositional outliers and based on median absolute deviation (MAD) and correlation median. The new method is first evaluated in a simulation study and then on real data sets. The algorithm requires considerably less computational time than other procedures already existing in literature, it works well for huge compositional data sets at any level of contamination.