Journal of the Korean Statistical Society

  • 제22권2호
  • /
  • Pages.353-359
  • /
  • 1993
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

A Note on the Invariance Principle for Associated Sequences

  • Kim, Tae-Sung (Department of Statistics, Won-Kwang University, Iri 540-749) ;
  • Han, Kwang-Hee (Department of Computer Science, Chun-buk San Up University, Kunsan 573-400)
  • 발행 : 1993.12.01
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초록

In this note we consider other type of tightness than that of Birkel (1988) and prove an invariance principle for nonstationary associated processes by an application of the central limit theorem of Cox and Grimmett (1984), thus avoiding the argument of uniform integrability. This result is an extension to the nonstationary case of an invariance priciple of Newman and Wright (1981) as well as an improvement of the central limit theorem of Cox and Grimmett (1984).

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참고문헌

  1. Convergence of Probability Measure Billingsley,P.
  2. Stochastic Processes and Their Applcations v.27 The invariance principle for associated processes Birkel
  3. Pacific Journal of Mathmatics v.132 An invariance principle for associated random fields Burton,R.M.;Kim,T.S.
  4. The Annals of Probability v.12 Central limit theorems for associated random variables and percolation model Cox,J.T.;Grimmet,G.
  5. Annals of Mathematical Statistics v.38 Association of random variables with applications Esary,J.;Proschan,F.;Walkup,D.
  6. Communications in Mathematical Physics v.74 Normal fluctuations and the FKG inequalities Newman,C.M.
  7. Inequalities in Statistics and Probability v.5 Asymptotic independence and limit theorem for positively and negatively dependent random variables Newman,C.M.;Y.L.Tong(ed.)
  8. The Annals of Probability v.9 An invariance principle for certain dependent sequences Newman,C.M.;Wright,A.L.
  9. Zeitschrift fur Wahrscheinlichkeits Theorie and Verwande Gebiete v.59 Associated random variables and martingale inequalities Newman,C.M.;Wright,A.L.