Contributions for the detection of multivariate outliers

The detection of outliers in multivariate models is always a dicult matter, but the
subject is even more complex when dealing with dependent structures, as it is the case
with the Simultaneous Equation Model (SEM). Unlike other models dened by systems
of equations, such as the multivariate regression, the SEM assumes that the response
variable in each equation can be stated as an explanatory variable in the rest of the
system, meaning that explanatory variables can be correlated with the error terms. We
present a method of outlier detection that bypasses those diculties using the asymptotic
distribution of adequate robust Mahalanobis distances. The process identies anomalous
data points as outliers of the SEM in simple steps and it provides a clear visualization.
We illustrate this procedure with a real econometric data set.