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Bump hunting by topological data analysis
Felix Bernstein Institute for Mathematical Statistics in the Biosciences, University of Göttingen, Göttingen, Germany.
School of Dentistry, University of Alberta, Edmonton, Canada.
Department of Mathematics and Statistics, University of Guelph, Guelph, Canada.
Örebro University, School of Medical Sciences.ORCID iD: 0000-0003-2437-1300
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2017 (English)In: Stat, E-ISSN 2049-1573, Vol. 6, no 1, p. 462-471Article in journal (Refereed) Published
Abstract [en]

A topological data analysis approach is taken to the challenging problem of finding and validating the statistical significance of local modes in a data set. As with the SIgnificance of the ZERo (SiZer) approach to this problem, statistical inference is performed in a multi-scale way, that is, across bandwidths. The key contribution is a twoparameter approach to the persistent homology representation. For each kernel bandwidth, a sub-level set filtration of the resulting kernel density estimate is computed. Inference based on the resulting persistence diagram indicates statistical significance of modes. It is seen through a simulated example, and by analysis of the famous Hidalgo stamps data, that the new method has more statistical power for finding bumps than SiZer.

Place, publisher, year, edition, pages
John Wiley & Sons, 2017. Vol. 6, no 1, p. 462-471
Keywords [en]
Bootstrap, kernel density estimation, mode hunting, persistent homology, SiZer
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:oru:diva-65213DOI: 10.1002/sta4.167ISI: 000441301200019Scopus ID: 2-s2.0-85051252789OAI: oai:DiVA.org:oru-65213DiVA, id: diva2:1185425
Note

Funding Agencies:

Studienstiftung des Deutschen Volkes  

Natural Sciences and Engineering Research Council of Canada  DG 293180 

McIntyre Memorial Fund  

US National Science Foundation  IIS-1633074 

Available from: 2018-02-24 Created: 2018-02-24 Last updated: 2018-08-27Bibliographically approved

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Rush, Stephen

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • nn-NB
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  • Other locale
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