A Cramér–von Mises Test of Uniformity on the Hypersphere (original) (raw)

Abstract

Testing uniformity of a sample supported on the hypersphere is one of the first steps when analysing multivariate data for which only the directions (and not the magnitudes) are of interest. In this work, a projection-based Cramér–von Mises test of uniformity on the hypersphere is introduced. This test can be regarded as an extension of the well-known Watson test of circular uniformity to the hypersphere. The null asymptotic distribution of the test statistic is obtained and, via numerical experiments, shown to be tractable and practical. A novel study on the uniformity of the distribution of craters on Venus illustrates the usage of the test.

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Acknowledgements

The first author acknowledges financial support from grants PGC2018-097284-B-I00, IJCI-2017-32005 and MTM2016-76969-P, funded by the Spanish Ministry of Economy, Industry and Competitiveness, and the European Regional Development Fund. The second and third authors acknowledge financial support from grant MTM2017-86061-C2-2-P from the Spanish Ministry of Economy, Industry and Competitiveness. The authors gratefully acknowledge the computing resources of the Supercomputing Center of Galicia (CESGA). Comments by two referees are acknowledged.

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Authors and Affiliations

  1. Department of Statistics, Carlos III University of Madrid, Leganés, Spain
    Eduardo García-Portugués
  2. Department of Mathematics, Statistics and Computer Science, University of Cantabria, Santander, Spain
    Paula Navarro-Esteban & Juan Antonio Cuesta-Albertos

Authors

  1. Eduardo García-Portugués
  2. Paula Navarro-Esteban
  3. Juan Antonio Cuesta-Albertos

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Correspondence toEduardo García-Portugués .

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Editors and Affiliations

  1. Department of Economics and Law, University of Cassino and Southern Lazio, Cassino, Italy
    Simona Balzano
  2. Department of Economics and Law, University of Cassino and Southern Lazio, Cassino, Italy
    Giovanni C. Porzio
  3. Department of Economics and Law, University of Cassino and Southern Lazio, Cassino, Italy
    Renato Salvatore
  4. Department of Political Science, University of Naples Federico II, Naples, Italy
    Domenico Vistocco
  5. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy
    Maurizio Vichi

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García-Portugués, E., Navarro-Esteban, P., Cuesta-Albertos, J.A. (2021). A Cramér–von Mises Test of Uniformity on the Hypersphere. In: Balzano, S., Porzio, G.C., Salvatore, R., Vistocco, D., Vichi, M. (eds) Statistical Learning and Modeling in Data Analysis. CLADAG 2019. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-030-69944-4\_12

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