Communications for Statistical Applications and Methods

  • 제16권4호
  • /
  • Pages.687-696
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  • 2009
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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A Central Limit Theorem for the Linear Process in a Hilbert Space under Negative Association

  • Ko, Mi-Hwa (Department of Mathematics and Institute of Basic Natural Science, WonKwang University)
  • 발행 : 2009.07.31
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초록

We prove a central limit theorem for the negatively associated random variables in a Hilbert space and extend this result to the linear process generated by negatively associated random variables in a Hilbert space. Our result implies an extension of the central limit theorem for the linear process in a real space under negative association to a simplest case of infinite dimensional Hilbert space.

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참고문헌

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  2. Billingsley, P. (1968). Convergence of Probability Measures, John Wiley & Sons, New York
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  8. Kim, T. S. and Ko, M. H. (2008). A central limit theorem for the linear process generated by associated random variables in a Hilbert space, Statistics & Probability Letters, 78, 2102-2109 https://doi.org/10.1016/j.spl.2008.01.079
  9. Kim, T. S., Ko, M. H. and Han, K. H. (2008). On the almost sure convergence for a linear process generated by negatively associated random variables in a Hilbert space, Statistics & Probability Letters, 78, 2110-2115 https://doi.org/10.1016/j.spl.2008.01.082
  10. Ko, M. H. (2006). Functional central limit theorems for multivariate linear processes generated by dependent random vectors, Communications of the Korean Mathematical Society, 21, 779-786 https://doi.org/10.4134/CKMS.2006.21.4.779
  11. Ko, M. H., Kim, T. S. and Han, K. H. (2009). A note on the almost sure convergence for dependent random variables in a Hilbert space, Journal of Theoretical Probability, 22, 506-513 https://doi.org/10.1007/s10959-008-0144-z
  12. Ko, M. H., Ryu, D. H. and Han, K. H. (2006). A central limit theorem for moving average process with negatively associated innovation, International Mathematical Forum, 1, 492-502
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피인용 문헌

  1. A STRONG LAW OF LARGE NUMBERS FOR AANA RANDOM VARIABLES IN A HILBERT SPACE AND ITS APPLICATION vol.32, pp.1, 2010, https://doi.org/10.5831/HMJ.2010.32.1.091