Multivariate outlier detection in Stata

Before implementing any multivariate statistical analysis based on empirical covariance matrices, it is important to check whether outliers are present because their existence could induce significant biases. In this article, we present the minimum covariance determinant estimator, which is commonly used in robust statistics to estimate location parameters and multivariate scales. These estimators can be used to robustify Mahalanobis distances and to identify outliers. Verardi and Croux (1999, Stata Journal 9: 439-453; 2010, Stata Journal 10: 313) programmed this estimator in Stata and made it available with the mcd command. The implemented algorithm is relatively fast and, as we show in the simulation example section, outperforms the methods already available in Stata, such as the Hadi method.