zbMATH — the first resource for mathematics

The unifying role of iterative generalized least squares in statistical algorithms. With comments by Bent Jørgensen, Peter McCullagh, Joe R. Hill and a rejoinder by the author. (English) Zbl 0955.62607
Summary: This expository paper deals with the role of iterative generalized least squares as an algorithm for the computation of statistical estimators. Relationships between various algorithms, such as Newton-Raphson, Gauss-Newton, and scoring, are studied. A parallel is made between statistical properties of the model and the structure of the numerical algorithm employed to find parameter estimates. In particular, a general linearizability property that extends the concept of link function in generalized linear models is considered and its computational meaning is discussed. Maximum quasilikelihood estimators are reinterpreted so that they may exist even when there is no quasilikelihood function.

62J05 Linear regression; mixed models
62A01 Foundations and philosophical topics in statistics
62F10 Point estimation
Full Text: DOI