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Testing Circular Antipodal Symmetry Through Data Depths

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Classification, (Big) Data Analysis and Statistical Learning

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Abstract

This work discusses how to test antipodal symmetry of circular distributions through depth functions. Two notions of depths for circular data are adopted, and their performances are evaluated and compared through a simulation study.

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References

  1. Agostinelli, C., Romanazzi, M.: Nonparametric analysis of directional data based on data depth. Environ. Ecol. Stat. 20, 253–270 (2013)

    Article  MathSciNet  Google Scholar 

  2. Jones, M.C., Pewsey, A.: Inverse Batschelet distributions for circular data. Biometrics 68, 183–193 (2012)

    Article  MathSciNet  Google Scholar 

  3. Jupp, P.E., Spurr, B.D.: Sobolev tests for symmetry of directional data. Ann. Stat. 11, 1225–1231 (1983)

    Article  MathSciNet  Google Scholar 

  4. Ley, C., Sabbah, C., Verdebout, T.: A new concept of quantiles for directional data and the angular Mahalanobis depth. Electr. J. Stat. 8, 795–816 (2014)

    Article  MathSciNet  Google Scholar 

  5. Ley, C., Verdebout, T.: Simple optimal tests for circular reflective symmetry about a specified median direction. Stat. Sin. 24, 1319–1339 (2014)

    MathSciNet  MATH  Google Scholar 

  6. Liu, R., Singh, K.: Ordering directional data: concepts of data depth on circles and spheres. Ann. Stat. 20, 1468–1484 (1992)

    Article  MathSciNet  Google Scholar 

  7. Moddares, R., Gastwirth, J.L.: A modified runs test for symmetry. Stat. Probab. Lett. 31, 107–112 (1996)

    Article  MathSciNet  Google Scholar 

  8. Pewsey, A.: Testing circular symmetry. Can. J. Stat. 30, 591–600 (2002)

    Article  MathSciNet  Google Scholar 

  9. Pewsey, A.: Testing for circular reflective symmetry about a known median axis. J. Appl. Stat. 31, 575–585 (2004)

    Article  MathSciNet  Google Scholar 

  10. Schach, S.: Nonparametric symmetry tests for circular distributions. Biometrika 56, 571–577 (1969)

    Article  MathSciNet  Google Scholar 

  11. Umbach, D., Jammalamadaka, S.R.: Building asymmetry into circular distributions. Stat. Probab. Lett. 79, 659–663 (2009)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Industrial Engineering, University of Naples Federico II, Naples, Italy

    Giuseppe Pandolfo

  2. Department of Economics and Law, University of Cassino and Southern Lazio, Cassino, Italy

    Giovanni Casale & Giovanni C. Porzio

Authors
  1. Giuseppe Pandolfo
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  2. Giovanni Casale
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  3. Giovanni C. Porzio
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Corresponding author

Correspondence to Giuseppe Pandolfo .

Editor information

Editors and Affiliations

  1. Department of Business and Economics, University of Cagliari, Cagliari, Italy

    Francesco Mola

  2. Department of Business and Economics, University of Cagliari, Cagliari, Italy

    Claudio Conversano

  3. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maurizio Vichi

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Pandolfo, G., Casale, G., Porzio, G.C. (2018). Testing Circular Antipodal Symmetry Through Data Depths. In: Mola, F., Conversano, C., Vichi, M. (eds) Classification, (Big) Data Analysis and Statistical Learning. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-55708-3_11

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