A multivariate Poisson model based on comonotonic shocks

Summary Multivariate count data arise naturally in practice. In analysing such data, it is critical to define a model that can accurately capture the underlying dependence structure between the counts. To this end, this paper develops a multivariate model wherein correlated Poisson margins are gener...

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Bibliographic Details
Published in:International statistical review 2021-08, Vol.89 (2), p.323-348
Main Authors: Schulz, Juliana, Genest, Christian, Mesfioui, Mhamed
Format: Article
Language:English
Subjects:
comonotonic shock
Convolution
correlation
dependence structure
Multivariate analysis
multivariate count data
multivariate Poisson model
positive quadrant dependence
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Summary:Summary Multivariate count data arise naturally in practice. In analysing such data, it is critical to define a model that can accurately capture the underlying dependence structure between the counts. To this end, this paper develops a multivariate model wherein correlated Poisson margins are generated by a comonotonic shock vector. The proposed model allows for greater flexibility in the dependence structure than that of the classical construction, which relies on the convolution of vectors of common Poisson shock variables. Several probabilistic properties of the multivariate comonotonic shock Poisson model are established, and various estimation strategies are discussed in detail. The model is further studied through simulations, and its utility is highlighted using a real data application.
ISSN:0306-7734
1751-5823
DOI:10.1111/insr.12408