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Splitting models for multivariate count data

By Jean Peyhardi, Pierre Fernique and Jean-Baptiste Durand

Abstract

International audienceWe investigate the class of splitting distributions as the composition of a singular multivariate distribution and a univariate distribution. It will be shown that most common parametric count distributions (multinomial, negative multinomial, multivariate hypergeometric, multivariate negative hypergeometric, …) can be written as splitting distributions with separate parameters for both components, thus facilitating their interpretation, inference, the study of their probabilistic characteristics and their extensions to regression models. We highlight many probabilistic properties deriving from the compound aspect of splitting distributions and their underlying algebraic properties. Parameter inference and model selection are thus reduced to two separate problems, preserving time and space complexity of the base models. Based on this principle, we introduce several new distributions. In the case of multinomial splitting distributions, conditional independence and asymptotic normality properties for estimators are obtained. Mixtures of splitting regression models are used on a mango tree dataset in order to analyze the patchiness

Topics: Compound distribution, Multivariate extension, Probabilistic graphical model, Singular multivariate distribution, compound distribution, singular multivariate distribution, multivariate extension, probabilistic graphical model, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
Publisher: 'Elsevier BV'
Year: 2021
DOI identifier: 10.1016/j.jmva.2020.104677
OAI identifier: oai:HAL:hal-02962877v1
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