Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Validity of the formal Edgeworth expansion when the underlying distribution is partly discrete
Download PDF
Download PDF
  • Published: May 1989

Validity of the formal Edgeworth expansion when the underlying distribution is partly discrete

  • J. L. Jensen1 

Probability Theory and Related Fields volume 81, pages 507–519 (1989)Cite this article

  • 141 Accesses

  • 6 Citations

  • Metrics details

Summary

Validity of the formal Edgeworth expansion for the distribution of the statistic √ng(X n /n, Y n /n) is considered. Here X n is a continuous variate and Y n is a discrete variate. In general if (X n , Y n ) resemble the sum of i.i.d. variables and the partial derivative of g with respect to the first variable has full rank it is possible to establish an Edgeworth expansion.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Bartlett, M.S.: The characteristic function of a conditional statistic. J. London Math. Soc. 13, 62–67 (1938)

    Google Scholar 

  2. Bhattacharya, R.N., Ghosh, J.K.: On the validity of the formal Edgeworth expansion. Ann. Stat. 6, 434–451 (1978)

    Google Scholar 

  3. Bhattacharya, R.N., Ranga Rao, R.: Normal Approximations and Asymptotic Expansions. New York: Wiley 1976

    Google Scholar 

  4. Götze, F., Hipp, C.: Asymptotic expansions in the central limit theorem under moment conditions. Z. Wahrscheinlichkeitstheor. Verw. Geb. 42, 67–87 (1978)

    Google Scholar 

  5. Hipp, C.: Asymptotic expansions for conditional distributions: the lattice case. Probab. Math. Stat. 4, 207–219 (1984)

    Google Scholar 

  6. Jensen, J.L.: Standardized log likelihood ratio statistic for mixtures of discrete and continuous observations. Ann. Stat. 15, 314–324 (1987a)

    Google Scholar 

  7. Jensen, J.L.: On asymptotic expansions in non-ergodic models. Scand. J. Stat. 14, 305–318 (1987b)

    Google Scholar 

  8. Jensen, J.L.: A note on asymptotic expansions for Markov chains using operator theory. Adv. Appl. Math. 8, 377–392 (1987c)

    Google Scholar 

  9. Jensen, J.L.: Asymptotic expansions for strongly mixing Harris recurrent Markov chains. Scand. J. Stat. 16, 47–64 (1989)

    Google Scholar 

  10. Sargan, J.D.: Econometric estimators and the Edgeworth expansion. Econometrica 44, 421–448 (1976)

    Google Scholar 

  11. Skovgaard, I.M. Transformation of an Edgeworth expansion by a sequence of smooth functions. Scand. J. Stat. 8, 207–217 (1981)

    Google Scholar 

  12. Skovgaard, I.M.: On multivariate Edgeworth expansions. Int. Stat. Rev. 54, 169–186 (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, Ny Munkegade, DK-8000, Aarhus C, Denmark

    J. L. Jensen

Authors
  1. J. L. Jensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jensen, J.L. Validity of the formal Edgeworth expansion when the underlying distribution is partly discrete. Probab. Th. Rel. Fields 81, 507–519 (1989). https://doi.org/10.1007/BF00367300

Download citation

  • Received: 02 June 1986

  • Revised: 29 August 1988

  • Issue Date: May 1989

  • DOI: https://doi.org/10.1007/BF00367300

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Continuous Variate
  • Stochastic Process
  • Partial Derivative
  • Probability Theory
  • Statistical Theory
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature