Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/81782

Title

Vector generalized linear and additive extreme value models

Author(s)

Yee, Thomas W.;  Stephenson, Alec G.

Abstract

Over recent years parametric and nonparametric regression has slowly been adopted into extreme value data analysis. Its introduction has been characterized by piecemeal additions and embellishments, which has had a negative effect on software development and usage. The purpose of this article is to convey the classes of vector generalized linear and additive models (VGLMs and VGAMs) as offering significant advantages for extreme value data analysis, providing flexible smoothing within a unifying framework. In particular, VGLMs and VGAMs allow all parameters of extreme value distributions to be modelled as linear or smooth functions of covariates. We implement new auxiliary methodology by incorporating a quasi-Newton update for the working weight matrices within an iteratively reweighted least squares (IRLS) algorithm. A software implementation by the first author, called the vgam package for r, is used to illustrate the potential of VGLMs and VGAMs.

Publication type

Journal article

Source

Extremes, Vol. 10, no. 1 (Jun 2007), pp. 1-19

Publication year

2007

FOR Code(s)

01 Mathematical Sciences

Keyword(s)

Extreme value modelling;  Fisher scoring;  Iteratively reweighted least squares;  Maximum likelihood estimation;  Penalized likelihood;  Smoothing;  Vector splines

Publisher

Springer

ISSN

1386-1999

Publisher URL

http://dx.doi.org/10.1007/s10687-007-0032-4

Copyright

Copyright © 2007 Springer Science + Business Media, LLC.

Peer reviewed