# What are the assumptions for multivariate outlier detection using Minimum Covariance Determinant (MCD)

Currently I am working on multivariate outlier detection. I would like to try some statistical methods, such as the Minimum Covariance Determinant (MCD) method, to identify the outliers.

In my data set, some of the variables do not follow certain distributions, say the Gaussian distribution. Therefore, I am wondering whether it is valid to use the Minimum Covariance Determinant method in this case, to identify multivariate outliers. In another word, what are the basic assumptions for using MCD to detect multivariate outliers?

The (Fast)-MCD algorithm looks for the $h$ observations with smallest scatter. The determinant of the covariance matrix is a good measure of scatter of a cloud of points when that cloud of points (in this case the $h$ most central observations) is symmetrically distributed around a centre.