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An almost sure central limit theorem for the weight function sequences of NA random variables

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Abstract

Consider the weight function sequences of NA random variables. This paper proves that the almost sure central limit theorem holds for the weight function sequences of NA random variables. Our results generalize and improve those on the almost sure central limit theorem previously obtained from the i.i.d. case to NA sequences.

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References

  1. Billingsley P, Convergence of probability measures (New York: Wiley) (1968)

    MATH  Google Scholar 

  2. Brosamler G A, An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc. 104 (1988) 561–574

    Article  MathSciNet  MATH  Google Scholar 

  3. Chandrasekharan K and Minakshisundaram S, Typical means (Oxford: Oxford University Press) (1952)

    MATH  Google Scholar 

  4. Hörmann S, Optimal averaging procedures in almost sure cenrtal limit theory, Metodološki zvezki. 2(2) (2005) 271–282

    Google Scholar 

  5. Ibragimov I A and Lifshits M, On the convergence of generalized moments in almost sure central limit theorem, Statist. Probab. Lett. 40 (1998) 343–351

    Article  MathSciNet  MATH  Google Scholar 

  6. Joag-Dev K and Proschan F, Negative association of random variables with applications, Ann. Statist. 11(1) (1983) 286–295

    Article  MathSciNet  MATH  Google Scholar 

  7. Lacey M T and Philipp W, A note on the almost sure central limit theorem, Statist. Probab. Lett. 9 (1990) 201–205

    Article  MathSciNet  MATH  Google Scholar 

  8. Matula P A, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett. 15 (1992) 209–213

    Article  MathSciNet  MATH  Google Scholar 

  9. Miao Y, Central limit theorem and almost sure central limit theorem for the product of some partial sums, Proc. Indian Acad. Sci. (Math. Sci.) 118(2) (2008) 289–294

    Article  MathSciNet  MATH  Google Scholar 

  10. Peligrad M and Shao Q M, A note on the almost sure central limit theorem for weakly dependent random variables, Statist. Probab. Lett. 22 (1995) 131–136

    Article  MathSciNet  MATH  Google Scholar 

  11. Schatte P, On strong versions of the central limit theorem, Math. Nachr. 137 (1988) 249–256

    Article  MathSciNet  MATH  Google Scholar 

  12. Shao Q M, A comparison theorem on moment inequalities between negatively associated and independent random variables, J. Theor. Probab. 13(2) (2000) 343–356

    Article  MATH  Google Scholar 

  13. Su C and Chi X, Some results on CLT for non-stationary NA sequences, Acta Math. Appl. Sin. 21(1) (1988) 9–21 (in Chinese)

    MathSciNet  Google Scholar 

  14. Wu Q Y, Strong consistency of M estimator in linear model for negatively associated samples, J. Syst. Sci. Complex. 19(4) (2006) 592–600

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu Q Y and Jiang Y Y, A law of the iterated logarithm of partial sums for NA random variables, J. Korean Stat. Soc. 39(2) (2010a) 199–206

    Article  MathSciNet  Google Scholar 

  16. Wu Q Y and Jiang Y Y, Chover’s law of the iterated logarithm for NA sequences, J. Syst. Sci. Complex. 23(2) (2010b) 293–302

    Article  MathSciNet  MATH  Google Scholar 

  17. Wu Q Y, Almost sure limit theorems for stable distribution, Stat. Probab. Lett. 81(6) (2011) 662–672

    Article  MATH  Google Scholar 

  18. Zhang L X, The weak convergence for functions of negatively associated random variables, J. Multivariate Anal. 78 (2001) 272–298

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Qunying Wu.

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Wu, Q. An almost sure central limit theorem for the weight function sequences of NA random variables. Proc Math Sci 121, 369–377 (2011). https://doi.org/10.1007/s12044-011-0036-5

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  • DOI: https://doi.org/10.1007/s12044-011-0036-5

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