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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.

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  • $\begingroup$ Do you know the distribution of $E$? $\endgroup$ – jbowman Aug 9 '19 at 15:27
  • $\begingroup$ Yes, multivariate normal distribution. $\endgroup$ – Wagner Jorge Aug 9 '19 at 15:34
  • $\begingroup$ 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! $\endgroup$ – jbowman Aug 9 '19 at 15:51
  • $\begingroup$ I can't use a similar approach, because I need a methodology to build outliers. I will use in my thesis. $\endgroup$ – Wagner Jorge Aug 9 '19 at 16:31

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