Application of distance standard deviation in functional data analysis

Mirosław Krzyśko () and Łukasz Smaga ()
Additional contact information
Mirosław Krzyśko: Calisia University-Kalisz
Łukasz Smaga: Adam Mickiewicz University

Advances in Data Analysis and Classification, 2024, vol. 18, issue 2, No 9, 454 pages

Abstract: Abstract This paper concerns the measurement and testing of equality of variability of functional data. We apply the distance standard deviation constructed based on distance correlation, which was recently introduced as a measure of spread. For functional data, the distance standard deviation seems to measure different kinds of variability, not only scale differences. Moreover, the distance standard deviation is just one real number, and for this reason, it is of more practical value than the covariance function, which is a more difficult object to interpret. For testing equality of variability in two groups, we propose a permutation method based on centered observations, which controls the type I error level much better than the standard permutation method. We also consider the applicability of other correlations to measure the variability of functional data. The finite sample properties of two-sample tests are investigated in extensive simulation studies. We also illustrate their use in five real data examples based on various data sets.

Keywords: Distance correlation; Functional data analysis; Projection correlation; Standard deviation; Variability measure; 62R10; 62H15 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11634-023-00538-6 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:advdac:v:18:y:2024:i:2:d:10.1007_s11634-023-00538-6

Ordering information: This journal article can be ordered from
http://www.springer. ... ds/journal/11634/PS2

DOI: 10.1007/s11634-023-00538-6

Access Statistics for this article

Advances in Data Analysis and Classification is currently edited by H.-H. Bock, W. Gaul, A. Okada, M. Vichi and C. Weihs

More articles in Advances in Data Analysis and Classification from 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)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().