Splitting models for multivariate count data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:181

Article

Peyhardi, Jean¹  Fernique, Pierre²  Durand, Jean-Baptiste³ 

[1] Univ Montpellier, CNRS, IMAG, F-34090 Montpellier, France

[2] Chappes Res Ctr, Limagrain Field Seeds Res, Biostat Dept, Chappes, France

[3] Univ Grenoble Alpes, CNRS, Grenoble INP, INRIA,Inst Engn,LJK, F-38000 Grenoble, France

关键词: Compound distribution;    Multivariate extension;    Probabilistic graphical model;    Singular multivariate distribution;   

DOI  :  10.1016/j.jmva.2020.104677

来源: Elsevier

【 摘 要 】

We 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free