In reply to Peter Flom.

Briefly, there are multivariate outliers and there are univariate (in general, lower-dimensional) outliers. You can have a MV outlier that is not a univariate outlier in any coordinate, such as your 12-year-old widow. You can also have univariate outliers that are not MV outliers.

For highly correlated data, the data will mostly lie in a lower-dimensional subspace. You can use principal components to reduce the dimensionality to a linear subspace. Then you can classify outliers that are within the subspace but away from the center, or you can have outliers that are near the center but are off the subpace. Or both. The geometry of the MV case very rich, indeed.