## Statistical Science

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

### The Unifying Role of Iterative Generalized Least Squares in Statistical Algorithms

#### 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.

#### 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.Project Euclid: euclid.ss/1177012409
- 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.Project Euclid: euclid.ss/1177012410
- 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.Project Euclid: euclid.ss/1177012411
- 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.Project Euclid: euclid.ss/1177012412