The “classical” \(\psi\)-function cPsi can be
used to get a non-robust, i.e., classical, fit. The psi slot equals
the identity function, and the rho slot equals quadratic function.
Accordingly, the robustness weights will always be 1 when using cPsi.
The Huber \(\psi\)-function huberPsi is identical to
the one in the package robustbase. The psi slot equals the
identity function within \(\pm k\) (where \(k\) is the tuning
parameter). Outside this interval it is equal to \(\pm k\). The
rho slot equals the quadratic function within \(\pm k\) and a
linear function outside.
The smoothed Huber \(\psi\)-function is very similar to the
regular Huber \(\psi\)-function. Instead of a sharp bend like the
Huber function, the smoothed Huber function bends smoothly. The first tuning
contant, k, can be compared to the tuning constant of the original Huber
function. The second tuning constant, s, determines the smoothness of the
bend.