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A hierarchical model for non‐stationary multivariate extremes: a case study of surface‐level ozone and NO x data in the UK
Author(s) -
Eastoe Emma F.
Publication year - 2009
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.938
Subject(s) - univariate , multivariate statistics , bivariate analysis , extreme value theory , joint probability distribution , econometrics , marginal distribution , statistics , environmental science , generalized extreme value distribution , multivariate analysis , conditional probability distribution , computer science , meteorology , mathematics , geography , random variable
Within the last couple of decades much effort has been put into monitoring and analysing air pollution levels in an attempt to improve both our understanding of the scientific mechanisms involved and our ability to make predictions of future levels. In this paper we use extreme value methods to produce a statistical model for the joint distribution of surface‐level ozone (O 3 ), nitric oxide (NO) and nitrogen dioxide (NO 2 ) daily maxima, observed at a single urban location in the UK. Much recent work on the statistical analysis of extreme values has focused on methods for multivariate extremes, however, for all of the existing methods, it is unclear how to model non‐stationary data. By extending the pre‐processing method for the analysis of the extremes of non‐stationary univariate processes, we propose a hierarchical modelling approach for non‐stationary multivariate processes. This method allows prediction of the probabilities of any marginal or joint extreme events for non‐stationary multivariate data. We illustrate this by predicting marginal return levels for each of the pollutants of interest and then looking at the bivariate distribution of NO and NO 2 , conditional on ozone achieving a given marginal return level. Copyright © 2008 John Wiley & Sons, Ltd.