Numerical 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. This chapter considers some details of the iterative algorithms used to compute M‐estimators. It justifies the median polish method, which includes location as a special case. In the chapter, location and covariance are treated separately for the sake of simplicity. The chapter also talks about a very detailed treatment of the convergence of the iterative reweighting algorithm for simultaneous estimation. It deals with the descent algorithm, which coincides with the one for M‐estimators. In addition, the chapter considers the concentration step method for the trimmed least squares (LTS) estimator. It explains the normalized median (MADN) for solving converges.