Fit Robust

The Fit Robust option reduces the influence of outliers in the response variable. The Huber M-estimation method is used. Huber M-estimation finds parameter estimates that minimize the Huber loss function:

where

ei refers to the residuals

The Huber loss function penalizes outliers and increases as a quadratic for small errors and linearly for large errors. In the JMP implementation, k = 2. For more information about robust fitting, see Huber (1973) and Huber and Ronchetti (2009).