대한수학회지 (Journal of the Korean Mathematical Society)

  • 제49권2호
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  • Pages.235-249
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  • 2012
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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PRECISE ASYMPTOTICS OF MOVING AVERAGE PROCESS UNDER ?-MIXING ASSUMPTION

  • Li, Jie (School of Mathematics and Statistics Zhejiang University of Finance and Economics)
  • 투고 : 2010.09.25
  • 발행 : 2012.03.01
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초록

In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.

키워드

참고문헌

  1. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
  2. R. M. Burton and H. Dehling, Large deviations for some weakly dependent random process, Statist. Probab. Lett. 9 (1990), no. 5, 397-401. https://doi.org/10.1016/0167-7152(90)90031-2
  3. P. L. Hsu and H. Robbins, Complete convergence and the strong law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 25-31. https://doi.org/10.1073/pnas.33.2.25
  4. D. L. Li, M. B. Rao, and X. C. Wang, Complete convergence of moving average processes, Statist. Probab. Lett. 14 (1992), no. 2, 111-114. https://doi.org/10.1016/0167-7152(92)90073-E
  5. Y. X. Li, Precise asymptotics in the law of large numbers of moving-average processes, Acta Math. Sci. Ser. A Chin. Ed. 26 (2006), no. 5, 675-687.
  6. W. D. Liu and Z. Y. Lin, Precise asymptotics for a new kind of complete moment convergence, Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799. https://doi.org/10.1016/j.spl.2006.04.027
  7. Q. M. Shao, A moment inequality and its application, Acta Math. Sinica 31 (1988), no. 6, 736-747.
  8. X. Y. Yang, The law of the iterated logarithm and the central limit theorem with random indices for B-valued stationary linear processes, Chinese Ann. Math. Ser. A 17 (1996), no. 6, 703-714.
  9. L. X. Zhang, Complete convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 30 (1996), no. 2, 165-170. https://doi.org/10.1016/0167-7152(95)00215-4

피인용 문헌

  1. Precise asymptotics of complete moment convergence on moving average vol.28, pp.12, 2012, https://doi.org/10.1007/s10114-012-0355-1