IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v181y2021ics0047259x2030258x.html
   My bibliography  Save this article

Splitting models for multivariate count data

Author

Listed:
  • Peyhardi, Jean
  • Fernique, Pierre
  • Durand, Jean-Baptiste

Abstract

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.

Suggested Citation

  • Peyhardi, Jean & Fernique, Pierre & Durand, Jean-Baptiste, 2021. "Splitting models for multivariate count data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:jmvana:v:181:y:2021:i:c:s0047259x2030258x
    DOI: 10.1016/j.jmva.2020.104677
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X2030258X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2020.104677?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.
    2. Stoltenberg, Emil Aas & Hjort, Nils Lid, 2020. "Multivariate estimation of Poisson parameters," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Jones, M.C. & Marchand, Éric, 2019. "Multivariate discrete distributions via sums and shares," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 83-93.
    4. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.
    5. Fan Xia & Jun Chen & Wing Kam Fung & Hongzhe Li, 2013. "A Logistic Normal Multinomial Regression Model for Microbiome Compositional Data Analysis," Biometrics, The International Biometric Society, vol. 69(4), pages 1053-1063, December.
    6. J. Peyhardi & C. Trottier & Y. Guédon, 2015. "A new specification of generalized linear models for categorical responses," Biometrika, Biometrika Trust, vol. 102(4), pages 889-906.
    7. Peyhardi, Jean & Fernique, Pierre, 2017. "Characterization of convolution splitting graphical models," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 59-64.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bhat, Chandra R., 2022. "A closed-form multiple discrete-count extreme value (MDCNTEV) model," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 65-86.
    2. Paul Nailly & Etienne Côme & Latifa Oukhellou & Allou Samé & Jacques Ferriere & Yasmine Merad-Boudia, 2024. "Multivariate count time series segmentation with “sums and shares” and Poisson lognormal mixture models: a comparative study using pedestrian flows within a multimodal transport hub," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 455-491, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Castañer, Anna & Claramunt, M. Mercè & Lefèvre, Claude & Loisel, Stéphane, 2019. "Partially Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 47-58.
    2. Anna Casta~ner & M Merc`e Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Papers 1709.09955, arXiv.org.
    3. Anna Castañer & M Mercè Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Working Papers hal-01593552, HAL.
    4. Anna Castañer & M. Mercè Claramunt, 2019. "Equilibrium Distributions and Discrete Schur-constant Models," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 449-459, June.
    5. Claude Lefèvre & Matthieu Simon, 2021. "Schur-Constant and Related Dependence Models, with Application to Ruin Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 317-339, March.
    6. Duo Jiang & Thomas Sharpton & Yuan Jiang, 2021. "Microbial Interaction Network Estimation via Bias-Corrected Graphical Lasso," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 329-350, July.
    7. Jones, M.C. & Marchand, Éric, 2019. "Multivariate discrete distributions via sums and shares," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 83-93.
    8. Giguelay, J. & Huet, S., 2018. "Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 96-115.
    9. Can Cui & Susheela P. Singh & Ana‐Maria Staicu & Brian J. Reich, 2021. "Bayesian variable selection for high‐dimensional rank data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(7), November.
    10. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    11. Paul Nailly & Etienne Côme & Latifa Oukhellou & Allou Samé & Jacques Ferriere & Yasmine Merad-Boudia, 2024. "Multivariate count time series segmentation with “sums and shares” and Poisson lognormal mixture models: a comparative study using pedestrian flows within a multimodal transport hub," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 455-491, June.
    12. Srinivasan, Arun & Xue, Lingzhou & Zhan, Xiang, 2023. "Identification of microbial features in multivariate regression under false discovery rate control," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    13. Denuit, Michel & Liu, Liqun & Meyer, Jack, 2014. "A separation theorem for the weak s-convex orders," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 279-284.
    14. Kolev, Nikolai & Mulinacci, Sabrina, 2022. "New characterizations of bivariate discrete Schur-constant models," Statistics & Probability Letters, Elsevier, vol. 180(C).
    15. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.
    16. Denuit, Michel, 2016. "Risk Apportionment and Multiply Monotone Targets," LIDAM Discussion Papers ISBA 2016044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Stoltenberg, Emil Aas & Hjort, Nils Lid, 2020. "Multivariate estimation of Poisson parameters," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    18. Denuit, Michel M., 2018. "Risk apportionment and multiply monotone targets," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 74-77.
    19. Ta, Bao Quoc & Van, Chung Pham, 2017. "Some properties of bivariate Schur-constant distributions," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 69-76.
    20. Jean Peyhardi, 2020. "Robustness of Student link function in multinomial choice models," Post-Print hal-03227808, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:181:y:2021:i:c:s0047259x2030258x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.