A connection between half-quadratic criteria and EM algorithms

Iteratively Reweighted Least Squares (IRLS) and Residual Steepest descent (RSD) algorithms of robust statistics arise as special cases of half-quadratic schemes . Here, we adopt a statistical framework and we show that both algorithms are instances of the EM algorithm. The augmented dataset respectively involves a scale and a location mixture of Gaussians. The sufficient conditions for the construction cover a broad class of already known robust statistics.