Double folding test of unimodality with an application to invariant coordinate selection

Colombe Becquart, Aurore Archimbaud (), Anne M. Ruiz and Zaineb Smida ()
Additional contact information
Colombe Becquart: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Aurore Archimbaud: TBS - Toulouse Business School
Anne M. Ruiz: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Zaineb Smida: ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - CNRS - Centre National de la Recherche Scientifique

Working Papers from HAL

Abstract: Testing for unimodality is of particular interest in clustering, where multimodality can be viewed as evidence of an underlying group structure. The Double Folding Test of Unimodality (DFTU) was recently proposed as an extension of the Folding Test of Unimodality (FTU), but its original bivariate test statistic does not yield a straightforward global p-value. In this paper, we introduce a new test statistic for the DFTU that admits a well-defined p-value. We derive its asymptotic distribution, leading to a fast approximation of the p-value that avoids computationally intensive Monte Carlo procedures. We then apply the resulting test to component selection in invariant coordinate selection (ICS), a dimension reduction method. The aim is to identify the subspace containing the relevant clustering information and thereby improve the performance of subsequent clustering procedures. In this setting, multimodality offers a natural criterion for identifying informative components, as an alternative to the commonly used non-normality criterion. Applications show that the proposed unimodality-based criterion outperforms the normality-based criterion in identifying the subspace of interest in clustering settings.

Date: 2026-09
Note: View the original document on HAL open archive server: https://hal.science/hal-05746449v1
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-05746449v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-05746449

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().