A1 Refereed original research article in a scientific journal
Unsupervised linear discrimination using skewness
Authors: Radojičić, Una; Nordhausen, Klaus; Virta, Joni
Publisher: Academic Press
Publication year: 2026
Journal: Journal of Multivariate Analysis
Article number: 105524
Volume: 211
ISSN: 0047-259X
eISSN: 1095-7243
DOI: https://doi.org/10.1016/j.jmva.2025.105524
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.jmva.2025.105524
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/506160615
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
It is well-known that, in Gaussian two-group separation, the optimally discriminating projection direction can be estimated without any knowledge on the group labels. In this work, we gather several such unsupervised estimators based on skewness and derive their limiting distributions. As one of our main results, we show that all affine equivariant estimators of the optimal direction have proportional asymptotic covariance matrices, making their comparison straightforward. Two of our four estimators are novel and two have been proposed already earlier. We use simulations to verify our results and to inspect the finite-sample behaviors of the estimators.
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Funding information in the publication:
The work of JV was supported by the Research Council of Finland (Grants 335077, 347501, 353769). KN was supported by the HiTEc COST Action (CA21163) and by the Research Council of Finland (363261). The work of UR was supported by the Austrian Science Fund (FWF) , [10.55776/I5799].
