Faugeras, OlivierIdRef (2025) The Stick-Breaking and Ordering Representations of Compositional Data: Copulas and Regression models. Austrian Journal of Statistics, vol.55 (n°2). (In Press)

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Abstract

Compositional Data (CoDa) is usually viewed as data on the simplex and is studied via a log-ratio analysis, following the classical work of Aitchison (1986). We propose to bring to the fore an alternative view of CoDa as a stick breaking process, an approach which originates from Bayesian nonparametrics. The first stick-breaking approach gives rise to a view of CoDa as ordered statistics, from which we can derive “stick-ordered” distributions. The second approach is based on a rescaled stick-breaking transformation, and give rises to a geometric view of CoDa as a free unit cube. The latter allows to introduce copula and regression models, which are useful for studying the internal or external dependence of CoDa. These stick-breaking representations allow to effectively and simply deal with CoDa with zeroes. We establish connections with other topics of probability and statistics like i) spacings and order statistics, ii) Bayesian nonparametrics and Dirichlet distributions, iii) neutrality, iv) hazard rates and the product integral, v) mixability.

Item Type: Article
Language: English
Date: 2025
Refereed: Yes
Place of Publication: Vienna
Uncontrolled Keywords: compositional data analysis, stick-breaking representation, copula, regression, dis-tribution
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 12 May 2025 09:03
Last Modified: 13 May 2025 07:33
OAI Identifier: oai:tse-fr.eu:130539
URI: https://publications.ut-capitole.fr/id/eprint/50832

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