A Functional Central Limit Theorem for the Multivariate Linear Process Generated by Negatively Associated Random Vectors

  • Kim, Tae-Sung (Professor Division of Mathematics and Informational Statistics, Wonkwang University Iksan, Jeonbuk 570-749) ;
  • Seo, Hye-Young (Lecturer Division of Mathematics and Informational Statistics, WonKwang University IKsan, Jeongbu 570-749)
  • Published : 2001.12.01


A functional central limit theorem is obtained for a stationary multivariate linear process of the form (no abstract. see full-text) where{ $Z_{t}$} is a sequence of strictly stationary m-dimensional negatively associated random vectors with E $Z_{t}$=O and E∥ $Z_{t}$$^2$<$\infty$ and { $A_{u}$} is a sequence of coefficient matrices with (no abstract. see full-text) and (no abstract. see full-text).text).).



  1. Convergence of Probability measures Billingsley,P.
  2. Annal of Probability v.16 Moment bounds for associated sequences Birkel,T.
  3. Journal of Multivariate Analysis v.44 A functional central limit theorem for positively dependent random variables Birkel,P.
  4. Stochastic Processes and Applied v.23 An invariance principle for weakly associated random vectors Burton,R.M.;Dabrowski,A.D.;Dehling,H.
  5. Annals of Mathematical Statistics v.38 Association of random variables with applications Esary,J.;Proschan,F.;Walkup,D.
  6. Journal of Multivariate Analysis v.47 Sequential estimation of the mean vector of a multivariate linear process Fakhre Zakeri,I.;Lee,S.
  7. Journal of Statistics Plann & Inference v.83 On a functional limit theorems for multivariate linear with applications to sequential estimation Fakhre Zakeri,I.;Lee,S.
  8. Annals of Statistics v.11 Negative association of random variables with applications Joag Dev,K.;Proschan,F.
  9. Annals of Mathematical Statistics v.37 Some concepts of dependence Lehmann,E.L.
  10. Inequalities in Statistics and Probab. IMS Lecture Notes Monograph Series v.5 Asymptotic independence and limit theorems for positively and negatively dependent random variables Newman,C.M.
  11. Almost sure convergence Stout,W.