Estimation of the variance for strongly mixing sequences

  • Strongway Shi


Let {X n,n≥1∼ be a stationary strongly mixing random sequence satisfying EX 1=μ EX 1 2 <∞ and (VarS n )/nσ 2 as n→∞. In this paper a class of estimators of VarS n is studied. The weak consistency and asymptotic normality as well as the central limit theorem are presented

1991 MR Subject Classification

60F05 62F12 


Estimation strongly mixing consistency asymptotic normality 


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  1. 1.
    Peligrad, M. and Suresh, R., Estimation of variance of partial sums of an associated sequence of random variables, Stochastic Process. Appl., 1995, 56: 307–319.zbMATHCrossRefGoogle Scholar
  2. 2.
    Peligrad, M. and Shao, Q. M., Estimation of the variance of partial sums for π-mixing random variables, J. Multivariate Anal., 1995, 52: 140–157.zbMATHCrossRefGoogle Scholar
  3. 3.
    Peligrad, M. and Shao, Q. M., A note on estimation of variance for π-mixing sequences, Statist, and Probab. Lett., 1996, 26: 141–145.zbMATHCrossRefGoogle Scholar
  4. 4.
    Herrndorf, N., A functional central limit theorem for strongly mixing sequences of random variables, Z. Wahrsch. Verw. Gebiete, 1985, 69: 541–550.zbMATHCrossRefGoogle Scholar
  5. 5.
    Künsch, H.R., The jackknife and the bootstrap for general stationary observations, Ann. Statist. 1989, 17: 1217–1241.zbMATHGoogle Scholar
  6. 6.
    Carlstein, E., The use of subseries values for estimating the variance of a general statistic from a stationary sequence, Ann. Statist., 1986, 14: 1171–1179.zbMATHGoogle Scholar
  7. 7.
    Shao, Q. M. and Yu, H., Weak convergence for weighted empirical processes of dependent sequences, Ann. Probab., 1996, 24: 2098–2127.zbMATHCrossRefGoogle Scholar
  8. 8.
    Ibragimov, I. A. and Linnik, Yu. V., Independent and Stationary Sequences of Random Variables, Wolters, Groningen, 1971.zbMATHGoogle Scholar
  9. 9.
    Bradley, R. C. and Bryc, W., Multilinear forms and measures of dependence between random variables, J. Multivariate Anal., 1985, 16: 335–367.zbMATHCrossRefGoogle Scholar
  10. 10.
    Peligrad, M. and Utev, S., Central limit theorem for linear processes. Ann. Probab., 1997, 25: 443–456.zbMATHCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities 2000

Authors and Affiliations

  • Strongway Shi
    • 1
  1. 1.Dept. of Math.Zhejiang Univ.Hangzhou

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