The QUANTREG procedure uses robust multivariate location and scale estimates for leverage-point detection.

Mahalanobis distance is defined as

where and are the empirical multivariate location and scale, respectively. Here, does not include the intercept variable. The relationship between the Mahalanobis distance and the matrix is

Robust distance is defined as

where and are robust multivariate location and scale estimates that are computed according to the minimum covariance determinant (MCD) method of Rousseeuw and Van Driessen (1999).

These distances are used to detect leverage points. You can use the LEVERAGE and DIAGNOSTICS options in the MODEL statement
to request leverage-point and outlier diagnostics, respectively. Two new variables, `Leverage`

and `Outlier`

, respectively, are created and saved in an output data set that is specified in the OUTPUT statement.

Let be the cutoff value. The variable LEVERAGE is defined as

You can specify a cutoff value in the LEVERAGE option in the MODEL statement.

Residuals , that are based on quantile regression estimates are used to detect vertical outliers. The variable OUTLIER is defined as

You can specify the multiplier k of the cutoff value in the CUTOFF= option in the MODEL statement. You can specify the scale in the SCALE= option in the MODEL statement. By default, k = 3 and the scale is computed as the corrected median of the absolute residuals:

where is an adjustment constant for consistency when the normal distribution is used.

An ODS table called DIAGNOSTICS contains the `Leverage`

and `Outlier`

variables.