S-estimator

The goal of S-estimators is to have a simple high-breakdown regression estimator, which share the flexibility and nice asymptotic properties of M-estimators. The name "S-estimators" was chosen as they are based on estimators of scale.
We will consider estimators of scale defined by a function, which satisfy

For any sample of real numbers, we define the scale estimate as the solution of
where is the expectation value of for a standard normal distribution.
Definition:
Let be a sample of regression data with p-dimensional. For each vector, we obtain residuals by solving the equation of scale above, where satisfy R1 and R2. The S-estimator is defined by
and the final scale estimator is then