Simulate multivariate outliers

Considering a multivariate linear model $$\boldsymbol{Y = XB + E}$$, where $$\boldsymbol{Y, X, B}$$ and $$\boldsymbol{E}$$ have dimension $$n \times m$$, $$n \times p$$, $$p \times m$$ and $$n \times m$$, respectively.

I read in this page about outliers only in $$\boldsymbol{Y}$$, i.e. without considering $$\boldsymbol{X}$$.

However, I'd like to simulate outliers for $$\boldsymbol{Y}$$ considering the pair $$(\boldsymbol{Y, X})$$ to regression problem.

• Do you know the distribution of $E$? – jbowman Aug 9 '19 at 15:27
• Yes, multivariate normal distribution. – Wagner Jorge Aug 9 '19 at 15:34
• Then try simulating $E$ from the appropriate multivariate Normal, add some outliers to it, and calculate $Y_{sim}=X\beta+E_{sim}$ for whatever $X$ you are interested in simulating $Y$ for. How you add those outliers is likely to be the meat of whatever answer you accept! – jbowman Aug 9 '19 at 15:51
• I can't use a similar approach, because I need a methodology to build outliers. I will use in my thesis. – Wagner Jorge Aug 9 '19 at 16:31