Skip to main content
SpringerLink
Log in

Limit theorems for additive statistics based on moving average samples

  • Published:
Siberian Advances in Mathematics Aims and scope Submit manuscript

Abstract

We study statistics based on samples of moving averages generated by stationary sequence of random variables. The central limit theorem (CLT) is proved for sequences of observations defined by an analytic function of moving averages under consideration. For U- and V -statistics with canonical (degenerate) kernels, the limit distributions are studied.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.W. K. Andrews, “Nonstrong mixing autoregressive processes,” J. Appl. Probab. 21(4), 930–934 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  2. P. Billingsley, Convergence of ProbabilityMeasures (Wiley, New York, 1968).

    Google Scholar 

  3. I. S. Borisov and N. V. Volodko, “Orthogonal series and limit theorems for canonical U- and V -statistics of stationary connected observations,” Siberian Adv. Math. 18(4), 242–257 (2008).

    Article  MathSciNet  Google Scholar 

  4. J. Dedecker, F. Merlevede, and D. Volny, “On the weak invariance principle for non-adapted sequences under projective criteria,” J. Theoret. Probab. 20(4), 971–1004 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Doukhan, Mixing. Properties and Examples (Lecture Notes in Statistics 85, Springer, New York, 1994).

    MATH  Google Scholar 

  6. V. V. Gorodeckiĭ, “On the strong mixing property for linear sequences,” Teor. Veroyatn. Primen. 22(2), 421–423 (1977) [Theory Probab. Appl. 22 (2), 411–413 (1978)].

    Google Scholar 

  7. P. Hall and C. C. Heyde,Martingale Limit Theory and Its Application (Academic Press, New York, 1980).

    MATH  Google Scholar 

  8. H. C. Ho and T. Hsing, “Limit theorems for functionals of moving averages,” Ann. Probab. 25(4), 1636–1669 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  9. I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Sequences of Random Variables (Nauka, Moscow, 1965) [Noordhoff, Groningen, 1971].

    Google Scholar 

  10. F. Merlevede, M. Peligrad, and S. Utev, “Recent advances in invariance principles for stationary sequences,” Probab. Surv. 3, 1–36 (2006) (electronic).

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Rubin and R. Vitale, “Asymptotic distribution of symmetric statistics,” Ann. Statist. 8(1), 165–170 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  12. D. I. Sidorov, “On mixing conditions for sequences of moving averages,” Theory Probab. Appl. 54(2), 339–347 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  13. W. B. Wu, “Central limit theorems for functionals of linear processes and their applications,” Statist. Sinica 12(2), 635–649 (2002).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    I. S. Borisov & D. I. Sidorov

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    I. S. Borisov & D. I. Sidorov

Authors
  1. I. S. Borisov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. I. Sidorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. S. Borisov.

Additional information

Original Russian Text © I. S. Borisov and D. I. Sidorov, 2010, published in Matematicheskie Trudy, 2010, Vol. 13, No. 2, pp. 10–32.

About this article

Cite this article

Borisov, I.S., Sidorov, D.I. Limit theorems for additive statistics based on moving average samples. Sib. Adv. Math. 21, 233–249 (2011). https://doi.org/10.3103/S1055134411040018

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1055134411040018

Keywords

Search

Navigation