A1 Refereed original research article in a scientific journal
Metric Oja depth, new statistical tool for estimating the most central objects; 
Authors: Zamanifarizhandi, Vida; Virta, Joni
Publisher: Elsevier BV
Publication year: 2026
Journal: Computational Statistics and Data Analysis
Article number: 108447
Volume: 224
ISSN: 0167-9473
eISSN: 1872-7352
DOI: https://doi.org/10.1016/j.csda.2026.108447
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1016/j.csda.2026.108447
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/526966556
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
The Oja depth (simplicial volume depth) is one of the classical statistical techniques for measuring the central tendency of data in multivariate space. Despite the widespread emergence of object data like images, texts, matrices or graphs, a well-developed and suitable version of Oja depth for object data is lacking. To address this shortcoming, a novel measure of statistical depth, the metric Oja depth applicable to any object data, is proposed. Two competing strategies are used for optimizing metric depth functions, i.e., for finding the deepest objects among the sample. The performance of the metric Oja depth is compared with three other depth functions (half-space, lens, and spatial) in diverse data scenarios.
Keywords:
metric Oja depth, metric statistics, object data, optimisation, statistical depth
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Funding information in the publication:
The work of VZ was supported by the Finnish Doctoral Program Network in Artificial Intelligence, AI-DOC (decision number VN/3137/2024-OKM-6). The work of VZ and JV was supported by the Research Council of Finland (Grants 347501, 353769, 368494).
