Change-point detection in a tensor regression model

Mai Ghannam () and Sévérien Nkurunziza ()
Additional contact information
Mai Ghannam: University of Windsor
Sévérien Nkurunziza: University of Windsor

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 2, No 11, 609-630

Abstract: Abstract In this paper, we consider an inference problem in a tensor regression model with one change-point. Specifically, we consider a general hypothesis testing problem on a tensor parameter and the studied testing problem includes as a special case the problem about the absence of a change-point. To this end, we derive the unrestricted estimator (UE) and the restricted estimator (RE) as well as the joint asymptotic normality of the UE and RE. Thanks to the established asymptotic normality, we derive a test for testing the hypothesized restriction. We also derive the asymptotic power of the proposed test and we prove that the established test is consistent. Beyond the complexity of the testing problem in the tensor model, we consider a very general case where the tensor error term and the regressors do not need to be independent and the dependence structure of the outer-product of the tensor error term and regressors is as weak as that of an $$\mathcal {L}^2-$$ L 2 - mixingale. Further, to study the performance of the proposed methods in small and moderate sample sizes, we present some simulation results that corroborate the theoretical results. Finally, to illustrate the application of the proposed methods, we test the non-existence of a change-point in some fMRI neuro-imaging data.

Keywords: Asymptotic property; Inference; Change-point detection; Tensor regression; Multi-mode restrictions (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11749-023-00915-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:testjl:v:33:y:2024:i:2:d:10.1007_s11749-023-00915-5

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/11749/PS2

DOI: 10.1007/s11749-023-00915-5

Access Statistics for this article

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Alfonso Gordaliza and Ana F. Militino

More articles in TEST: An Official Journal of the Spanish Society of Statistics and Operations Research from Springer, Sociedad de Estadística e Investigación Operativa
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().