Skip to main content

Comments on: Tests for multivariate normality—a critical review with emphasis on weighted \(L^2\)-statistics

Abstract

We discuss extension of the BHEP test to more general families of distributions.

This is a preview of subscription content, access via your institution.

References

  1. Adler RJ, Feldman RE, Taqqu MS (1998) A practical guide to heavy tails: statistical techniques and applications. Birkhäuser, Boston

    MATH  Google Scholar 

  2. Berg C, Vignat C (2010) On the density of the sum of two independent student t-random vectors. Stat Probab Lett 80:1043–1055

    MathSciNet  Article  Google Scholar 

  3. Bonato M (2012) Modeling fat tails in stock returns: a multivariate stable-GARCH approach. Comput Stat 27:499–521

    MathSciNet  Article  Google Scholar 

  4. Epps TW (2005) Tests for location-scale families based on the empirical characteristic function. Metrika 62:99–114

    MathSciNet  Article  Google Scholar 

  5. Koutrouvelis IA, Meintanis SG (1999) Testing for stability based on the empirical characteristic function with applications to financial data. J Stat Comput Simul 64:275–300

    Article  Google Scholar 

  6. Kozubowski TJ, Podgórski K, Rychlik I (2013) Multivariate generalized laplace distribution and related random fields. J Multivar Anal 113:59–72

    MathSciNet  Article  Google Scholar 

  7. Matsui M, Takemura A (2008) Goodness-of-fit tests for symmetric stable distributions—empirical characteristic function approach. TEST 17:546–566

    MathSciNet  Article  Google Scholar 

  8. Meintanis SG (2005) Consistent tests for symmetric stability with finite mean based on the empirical characteristic function. J Stat Plan Inference 128:373–380

    MathSciNet  Article  Google Scholar 

  9. Meintanis SG, Ngatchou-Wandji J, Taufer E (2015) Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function. J Multivar Anal 140:171–192

    MathSciNet  Article  Google Scholar 

  10. Nadarajah S (2003) The Kotz-type distribution with applications. Statistics 37:341–358

    MathSciNet  Article  Google Scholar 

  11. Nolan JP (2013) Multivariate elliptically contoured stable distributions: theory and estimation. Comput Stat 28:2067–2089

    MathSciNet  Article  Google Scholar 

  12. Rachev S, Mittnik S (2000) Stable Paretian models in finance. Wiley, New York

    MATH  Google Scholar 

  13. Rossberg HJ (1995) Positive definite probability densities and probability distributions. J Math Sci 76:2181–2197

    MathSciNet  Article  Google Scholar 

  14. Samorodnitsky G, Taqqu MS (1994) Stable non-Gaussian random processes. Stochastic models with infinite variance. Chapman and Hall, New York

    MATH  Google Scholar 

  15. Uchaikin VV, Zolotarev VM (1999) Chance and stability. Stable distributions and their applications. VSP, Utrecht

    Book  Google Scholar 

  16. Ushakov NG (1999) Selected topics in characteristic functions. VSP, Utrecht

    Book  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Simos G. Meintanis.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Simos G. Meintanis: On sabbatical leave from the University of Athens.

This comment refers to the invited paper available at: https://doi.org/10.1007/s11749-020-00740-0.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Meintanis, S.G. Comments on: Tests for multivariate normality—a critical review with emphasis on weighted \(L^2\)-statistics. TEST 29, 898–902 (2020). https://doi.org/10.1007/s11749-020-00743-x

Download citation

Keywords

  • Characteristic function
  • Goodness-of-fit test
  • Alpha-stable distribution
  • Kotz-type distribution

Mathematics Subject Classification

  • Primary 62H15
  • Secondary 62G20