Skip to main content
Log in

Spherical symmetry: An elementary justification

  • Published:
Journal of the Italian Statistical Society Aims and scope Submit manuscript

Summary

The present paper includes characterizations of the conditions of spherical symmetry and of centered spherical symmetry. These characterizations provide an empirical justification for the above mentioned conditions of symmetry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Billingsely, P. (1986).Probability and Measure. Wiley, New York.

    Google Scholar 

  • Breiman, L. (1968).Probability. Addison-Wesley, Reading, Massachussetts.

    MATH  Google Scholar 

  • Bühlmann, H. (1958). Le problème “limite centrale” pour les variables aléatoire échangeables.C. R. Acad. Sci. Paris 246, 534–536.

    MATH  MathSciNet  Google Scholar 

  • Bühlmann, H. (1960). Austauschbare stochastische variabeln und ihre grenzwertsätze.Univ. Calif. Publ. Statist. 3, 1–35.

    Google Scholar 

  • Diaconis, P., Eaton, M. L., Lauritzen, S. L. (1992). Finite de Finetti theorems in linear models and multivariata analysis.Scand. Jour. Statist. 19, 289–315.

    MATH  MathSciNet  Google Scholar 

  • Eaton, M. L. (1989).Group Invariance Applications in Statistics. Regional Conference Series in Prob. and Statist., Vol. 1. IMS, ASA.

  • de Finetti, B. (1934), Come giustificare elementarmente la «legge normale» della probabilità?Periodico delle Matematiche Serie IV 14, 197–210. Reprint inArchimede 42 (1990), 51–64.

    MATH  Google Scholar 

  • de Finetti, B. (1938), Sur la condition d'equivalence partielle.Act. Scient. Ind. 739, 5–18.

    Google Scholar 

  • Kingman, J. F. C. (1972). On random sequences with spherical symmetry.Biometrika 59, 492–494.

    Article  MATH  MathSciNet  Google Scholar 

  • Link, G. (1980). Representation theorems of de Finetti type for (partially) symmetric probability measures. InStudies in Inductive Logic and Probability, II (C. Jeffrey, ed.) University of California Press, Berkley.

    Google Scholar 

  • Schoenberg, I. J. (1938). Metric spaces and positive definite functions.Trans. Amer. Math. Soc. 44, 522–536.

    Article  MATH  MathSciNet  Google Scholar 

  • Smith, A. F. M. (1981). On random sequences with centered spherical symmetry.J. R. Statist. Soc. B 43, 208–209.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eaton, M.L., Fortini, S. & Regazzini, E. Spherical symmetry: An elementary justification. J. It. Statist. Soc. 2, 1–16 (1993). https://doi.org/10.1007/BF02589072

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02589072

Keywords

Navigation