The ROBUSTREG Procedure |

Robust Distance |

The ROBUSTREG procedure uses the robust multivariate location and scale estimates for leverage-point detection. The procedure computes a robust version of the Mahalanobis distance by using the minimum covariance determinant (MCD) method of Rousseeuw (1984).

PROC ROBUSTREG implements the algorithm given by Rousseeuw and Van Driessen (1999) for MCD, which is similar to the algorithm for LTS.

The Mahalanobis distance is defined as

where and are the empirical multivariate location and scale. Here does not include the intercept. The relation between the Mahalanobis distance and the hat matrix is

The robust distance is defined as

where and are the robust multivariate location and scale obtained by MCD.

These distances are used to detect leverage points.

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