Statistical Science

The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms

Guido del Pino

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Abstract

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.

Article information

Source
Statist. Sci. Volume 4, Number 4 (1989), 394-403.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177012408

Digital Object Identifier
doi:10.1214/ss/1177012408

Mathematical Reviews number (MathSciNet)
MR1041764

Zentralblatt MATH identifier
0955.62607

JSTOR
links.jstor.org

Keywords
Iterative generalized least squares maximum likelihood estimation scoring algorithm quasilikelihood generalized linear models

Citation

del Pino, Guido. The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms. Statist. Sci. 4 (1989), no. 4, 394--403. doi:10.1214/ss/1177012408. https://projecteuclid.org/euclid.ss/1177012408.


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See also

  • See Comment: Bent Jorgensen. [The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms]: Comment. Statist. Sci., Volume 4, Number 4 (1989), 403--404.
  • See Comment: Peter McCullagh. [The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms]: Comment. Statist. Sci., Volume 4, Number 4 (1989), 404--405.
  • See Comment: Joe R. Hill. [The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms]: Comment. Statist. Sci., Volume 4, Number 4 (1989), 406--406.
  • See Comment: Guido del Pino. [The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms]: Rejoinder. Statist. Sci., Volume 4, Number 4 (1989), 407--408.