Iteratively Reweighted Least Squares for Maximum Likelihood Estimation, and Some Robust and Resistant Alternatives

Abstract

SUMMARY The scope of application of iteratively reweighted least squares to statistical estimation problems is considerably wider than is generally appreciated. It extends beyond the exponential-family-type generalized linear models to other distributions, to non-linear parameterizations, and to dependent observations. Various criteria for estimation other than maximum likelihood, including resistant alternatives, may be used. The algorithms are generally numerically stable, easily programmed without the aid of packages, and highly suited to interactive computation.