Kurtosis removal for data pre-processing

Nicola Loperfido

Advances in Data Analysis and Classification, 2023, vol. 17, issue 1, No 12, 239-267

Abstract: Abstract Mesokurtic projections are linear projections with null fourth cumulants. They might be useful data pre-processing tools when nonnormality, as measured by the fourth cumulants, is either an opportunity or a challenge. Nonnull fourth cumulants are opportunities when projections with extreme kurtosis are used to identify interesting nonnormal features, as for example clusters and outliers. Unfortunately, this approach suffers from the curse of dimensionality, which may be addressed by projecting the data onto the subspace orthogonal to mesokurtic projections. Nonnull fourth cumulants are challenges when using statistical methods whose sampling properties heavily depend on the fourth cumulant themselves. Mesokurtic projections ease the problem by allowing to use the inferential properties of the same methods under normality. The paper shows necessary and sufficient conditions for the existence of mesokurtic projections and compares them with other gaussianization methods. Theoretical and empirical results suggest that mesokurtic transformations are particularly useful when sampling from finite normal mixtures. The practical use of mesokurtic projections is illustrated with the AIS and the RANDU datasets.

Keywords: Closed skew-normal; Finite mixture; Gaussianization; High-dimensional; Kurtosis; Projection pursuit; 15A18; 62H10 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11634-022-00498-3 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:17:y:2023:i:1:d:10.1007_s11634-022-00498-3

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

DOI: 10.1007/s11634-022-00498-3

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 ().