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Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives. (English) Zbl 0555.62028

The paper offers an overview of the ”iteratively reweighted least squares” (IRLS) algorithm and its applications to statistical estimation problems for a number of various estimation criteria mentioned in the title. The wide applicability of IRLS rests on the fact that under many circumstances the Newton-Raphson and the scoring algorithm may be written down as an IRLS. A well known example is maximum likelihood estimation in generalized linear models.
The paper shows that IRLS can be applied to other models, to nonlinear parameterizations and to dependent observations. Some numerical properties of IRLS and numerically more stable variants, well known from numerical analysis, are discussed. Alternative optimization algorithms are mentioned shortly.
Reviewer: L.Fahrmeir

MSC:

62F10 Point estimation
62J99 Linear inference, regression
62J02 General nonlinear regression
65C99 Probabilistic methods, stochastic differential equations
62F35 Robustness and adaptive procedures (parametric inference)
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