Extremes

, Volume 10, Issue 1–2, pp 1–19 | Cite as

Vector generalized linear and additive extreme value models

Article

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 Open image in new window, is used to illustrate the potential of VGLMs and VGAMs.

Keywords

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

AMS 2000 Subject Classification

62P99 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of AucklandAucklandNew Zealand
  2. 2.Department of Statistics & Applied ProbabilityNational University of SingaporeSingaporeSingapore

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