IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v219y2025ics0167715224002943.html
   My bibliography  Save this article

Geometric quantile-based measures of multivariate distributional characteristics

Author

Listed:
  • Shin, Ha-Young
  • Oh, Hee-Seok

Abstract

Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes, and are easy to calculate. Some theoretical justification is given, followed by experiments illustrating that they are sensible measures of these distributional characteristics and some basic empirical justification for bootstrapped confidence regions.

Suggested Citation

  • Shin, Ha-Young & Oh, Hee-Seok, 2025. "Geometric quantile-based measures of multivariate distributional characteristics," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715224002943
    DOI: 10.1016/j.spl.2024.110325
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224002943
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110325?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. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Biman Chakraborty, 2001. "On Affine Equivariant Multivariate Quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 380-403, June.
    Full references (including those not matched with items on IDEAS)

    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. Andrea Meilán-Vila & Rosa M. Crujeiras & Mario Francisco-Fernández, 2024. "Nonparametric estimation for a functional-circular regression model," Statistical Papers, Springer, vol. 65(2), pages 945-974, April.
    2. Emilio Carrizosa & Jasone Ramírez-Ayerbe & Dolores Romero Morales, 2024. "A new model for counterfactual analysis for functional data," 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(4), pages 981-1000, December.
    3. Mohamed CHAOUCH & Ali GANNOUN & Jérôme SARACCO, 2008. "Conditional Spatial Quantile: Characterization and Nonparametric Estimation," Cahiers du GREThA (2007-2019) 2008-10, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    4. Smida, Zaineb & Laurent, Thibault & Cucala, Lionel, 2024. "A Hotelling spatial scan statistic for functional data: application to economic and climate data," TSE Working Papers 24-1583, Toulouse School of Economics (TSE).
    5. Nadja Klein & Thomas Kneib, 2020. "Directional bivariate quantiles: a robust approach based on the cumulative distribution function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 225-260, June.
    6. Chengxin Wu & Nengxiang Ling & Philippe Vieu & Guoliang Fan, 2025. "Composite quantile estimation in partially functional linear regression model with randomly censored responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(1), pages 28-47, March.
    7. Qiu, Zhiping & Fan, Jiangyuan & Zhang, Jin-Ting & Chen, Jianwei, 2024. "Tests for equality of several covariance matrix functions for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    8. Chaouch, Mohamed & Goga, Camelia, 2010. "Design-based estimation for geometric quantiles with application to outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2214-2229, October.
    9. Ma, Xuejun & Wang, Shaochen & Zhou, Wang, 2021. "Testing multivariate quantile by empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    10. Kokoszka, Piotr & Kulik, Rafał, 2023. "Principal component analysis of infinite variance functional data," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    11. Petersen, Alexander, 2024. "Mean and covariance estimation for discretely observed high-dimensional functional data: Rates of convergence and division of observational regimes," Journal of Multivariate Analysis, Elsevier, vol. 204(C).
    12. Caponera, Alessia & Panaretos, Victor M., 2022. "On the rate of convergence for the autocorrelation operator in functional autoregression," Statistics & Probability Letters, Elsevier, vol. 189(C).
    13. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    14. Mukhopadhyay, Nitai D. & Chatterjee, Snigdhansu, 2011. "High dimensional data analysis using multivariate generalized spatial quantiles," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 768-780, April.
    15. Silvia Novo & Germán Aneiros & Philippe Vieu, 2025. "Semi-functional partial linear regression with measurement error: an approach based on kNN estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(1), pages 235-261, March.
    16. Klaus Herrmann & Marius Hofert & Melina Mailhot, 2017. "Multivariate Geometric Expectiles," Papers 1704.01503, arXiv.org, revised Jan 2018.
    17. Shuquan Yang & Nengxiang Ling, 2025. "Robust estimation of functional factor models with functional pairwise spatial signs," Computational Statistics, Springer, vol. 40(1), pages 87-110, January.
    18. Valentina Masarotto & Guido Masarotto, 2024. "Covariance‐based soft clustering of functional data based on the Wasserstein–Procrustes metric," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 485-512, June.
    19. Agarwal, Gaurav & Tu, Wei & Sun, Ying & Kong, Linglong, 2022. "Flexible quantile contour estimation for multivariate functional data: Beyond convexity," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    20. Daniel Hlubinka & Lukáš Kotík & Miroslav Šiman, 2022. "Multivariate quantiles with both overall and directional probability interpretation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1586-1604, December.

    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:stapro:v:219:y:2025:i:c:s0167715224002943. 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.