Consider a multivariate contamination model, along the lines of Huber (1964), where with f1 being multi-normal while f2 is heavy-tailed multivariate probability density function, symmetric about θ....

Consider a multivariate contamination model, along the lines of Huber (1964), where

with f1 being multi-normal while f2 is heavy-tailed multivariate probability density function, symmetric about θ. Does f belong to the elliptically symmetric family? Does it belong to the diagonally symmetric family?