Skip to main content
SpringerLink
Log in
Book cover

Nonparametric Statistics for Stochastic Processes pp 15–37Cite as

Inequalities for mixing processes

  • Chapter

  • 464 Accesses

Part of the book series: Lecture Notes in Statistics ((LNS,volume 110))

Abstract

In this chapter we present some inequalities for covariances, joint densities and partial sums of stochastic discrete time processes when dependence is measured by strong mixing coefficients. The main tool is coupling with independent random variables. Some limit theorems for mixing processes are given as applications.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. BENNETT G. (1962). Probabihty inequalities for sum of independent random variables. J. Amer. Statis. Assoc. 57, 33–45

    Article  MATH  Google Scholar 

  2. BERBEE H.C.P.(1979) Random walks with stationary increments and renewal theory. Math. Centr. Tract. Amsterdam.

    Google Scholar 

  3. BILLINGSLEY P. (1968). Convergence of Probability Measures. Wiley

    MATH  Google Scholar 

  4. BILLINGSLEY P. (1986). Probability and Measure. edition. Wiley

    MATH  Google Scholar 

  5. BOSQ D. (1993). Bernstein-type large deviation inequalities for partial sums of strong mixing processs. Statistics, 24, 59–70.

    Article  MathSciNet  MATH  Google Scholar 

  6. BOSQ D. (1995). Optimal asymptotic quadratic error of density estimators for strong mixing or chaotic data. Statistics and Probability Letters. 22, 339–347.

    Article  MathSciNet  MATH  Google Scholar 

  7. BRADLEY R. (1983). Approximation theorems for strongly mixing random variables. Michigan Maths. J. 30, 69–81.

    Article  MathSciNet  MATH  Google Scholar 

  8. BRADLEY R. (1986). Basic Properties of strong mixing conditions, in E. EBERLEIN and M.S. TAQQU editors. Dependence in Probability and Statistics, p. 165–192. Birkhäuser.

    Google Scholar 

  9. CARBON M. (1993). Une nouvelle inégalité de grandes déviations. Applications. Pubi IRMA, Vol. 32 n° 11.

    Google Scholar 

  10. DAVYDOV Y.A. (1968). Convergence of distributions generated by stationary stochastic Processes. Theor. Probab. Appi. 13, 691–696.

    Article  MATH  Google Scholar 

  11. DOOB J.L. (1967). Stochastic Processes. (7th printing). Wiley

    Google Scholar 

  12. DOUKHAN P. (1994). Mixing -Properties and Examples. Lecture Notes in Statistics. Springer Verlag.

    Google Scholar 

  13. HOEFFDING (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13–30.

    Article  MathSciNet  MATH  Google Scholar 

  14. IBRAGIMOV LA. (1962). Some limits theorems for stationary Processes. Theor. Prob. Appi. 7, 349–382.

    Article  Google Scholar 

  15. PHAM D.T. — TRAN L.T. (1985). Some strong mixing properties of time series models. Stoch. Proc. Appi. 19, 207–303.

    MathSciNet  Google Scholar 

  16. RHOMARI N. (1994). Filtrage non paramétrique pour les processus non Markoviens. Applications. Ph D. Thesis University Pierre et Marie Curie (Paris).

    Google Scholar 

  17. RIO E. (1993). Covariance inequalities for strongly mixing processes. Ann. Inst. Henri Poincaré, 29, 4, 587–597.

    MathSciNet  MATH  Google Scholar 

  18. ROSENBLATT M. (1956). A central limit theorem and a strong mixing condition. Proc. Nat. Ac. Sc. USA, 42, 43–47.

    Article  MathSciNet  MATH  Google Scholar 

  19. STOUT W.F. (1974). Almost sure convergence. Academic Press.

    MATH  Google Scholar 

  20. TRAN L.T. (1989). The L convergence of kernel density estimates under dependence. The Ganad. J. of Statist. 17, 2, 197–208.

    MathSciNet  MATH  Google Scholar 

  21. YOKOYAMA R. (1980). Moments bound for stationary mixing sequences. Z. Wahrsch. Gebiete, 52, 45–57.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Statistique, Université Pierre et Marie Curie, 4 Place Jussieu, 75252, Paris cedex 05, France

    D. Bosq

Authors
  1. D. Bosq
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Bosq, D. (1996). Inequalities for mixing processes. In: Nonparametric Statistics for Stochastic Processes. Lecture Notes in Statistics, vol 110. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0489-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0489-0_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94713-6

  • Online ISBN: 978-1-4684-0489-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation