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
Berry-Esseen theorems for quadratic forms of Gaussian stationary processes
Download PDF
Download PDF
  • Published: June 1986

Berry-Esseen theorems for quadratic forms of Gaussian stationary processes

  • Masanobu Taniguchi1 

Probability Theory and Related Fields volume 72, pages 185–194 (1986)Cite this article

  • 126 Accesses

  • 7 Citations

  • Metrics details

Summary

LetX 1,X 2, ... be a Gaussian stationary process with spectral densityf(λ), and let

$$Z_j = \frac{1}{{\sqrt T }}\left\{ {\sum\limits_{l = 1}^{T - j + 1} {\left( {X_l X_{l + j - 1} - EX_l X_{l + j - 1} } \right)} } \right\}, j = 1,...,p.$$

The present paper gives a Berry-Esseen type theorem for the joint distribution of (Z 1, ...,Z p).

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Bhattacharya, R.N., Rao R.R.: Normal approximation and asymptotic expansions. New York: Wiley 1976

    Google Scholar 

  2. Brillinger, D.R.: Time series: data analysis and theory. New York: Holt 1975

    Google Scholar 

  3. Daniels, H.E.: The approximate distribution of serial correlation coefficients. Biometrika43, 169–185 (1956)

    Google Scholar 

  4. Does, R.J.M.M.: Berry-Esseen theorems for simple linear rank statistics under the null-hypothesis. Ann. Probab.10, 982–991 (1982)

    Google Scholar 

  5. Durbin, J.: Approximations for densities of sufficient estimators. Biometrika67, 311–333 (1980a)

    Google Scholar 

  6. Durbin, J.: The approximate distribution of partial serial correlation coefficients calculated from residuals from regression on Fourier series. Biometrika67, 335–349 (1980b)

    Google Scholar 

  7. Erickson, R.V.:L 1 bounds for asymptotic normality ofm-dependent sums using Stein's technique. Ann. Probab.2, 522–529 (1974)

    Google Scholar 

  8. Götze, F., Hipp, C.: Asymptotic expansions for sums of weakly dependent random vectors. Z. Wahrscheinlichkeitstheor. Verw. Geb.64, 211–239 (1983)

    Google Scholar 

  9. Helmers, R.: A Berry-Esseen theorem for linear combinations of order statistics. Ann. Probab.9, 342–347 (1981)

    Google Scholar 

  10. Taniguchi, M.: On the second order asymptotic efficiency of estimators of Gaussian ARMA processes. Ann. Stat.11, 157–169 (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, Faculty of Science, Hiroshima University, Higashi-Sendamachi, 730, Hiroshima, Japan

    Masanobu Taniguchi

Authors
  1. Masanobu Taniguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was partially supported by the Grant-in-Aid of the Ministry of Education

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Taniguchi, M. Berry-Esseen theorems for quadratic forms of Gaussian stationary processes. Probab. Th. Rel. Fields 72, 185–194 (1986). https://doi.org/10.1007/BF00699102

Download citation

  • Received: 15 January 1985

  • Revised: 01 October 1985

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00699102

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

  • Stochastic Process
  • Stationary Process
  • Probability Theory
  • Quadratic Form
  • Mathematical Biology
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