9Numerical Algorithms
Computing M‐estimators involves function minimization and/or solving nonlinear equations. General methods based on derivatives – like the Newton‐Raphson procedure for solving equations – are widely available, but they are inadequate for this specific type of problem, for the reasons given in Section 2.10.5.1.
In this chapter we consider some details of the iterative algorithms used to compute M‐estimators, as described in earlier chapters.
9.1 Regression M‐estimators
We shall justify the algorithm in Section 4.5 for solving (4.39); this includes location as a special case. Consider the problem
where
where 
and 
is any positive constant.
It is assumed that the 
are not collinear, otherwise there would be multiple solutions. It is assumed that 
is a 
‐function that the ...
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