A Weak Convergence for a Linear Process with Positive Dependent Sequences

  • Kim, Tae-Sung (Division of Mathematics & Informational Statistics and Institute of Basic Natural Science, Wonkwang University) ;
  • Ryu, Dae-Hee (Department of Computer Science, Chungwoon University) ;
  • Lee, Il-Hyun (Division of Mathematics & Informational Statistics and Institute of Basic Natural Science, Wonkwang University)
  • 발행 : 2002.12.01

초록

A weak convergence is obtained for a linear process of the form (equation omitted) where {$\varepsilon$$_{t}$ } is a strictly stationary sequence of associated random variables with E$\varepsilon$$_{t}$ = 0 and E$\varepsilon$$^{^2}$$_{t}$ < $\infty$ and {a $_{j}$ } is a sequence of real numbers with (equation omitted). We also apply this idea to the case of linearly positive quadrant dependent sequence.

키워드

참고문헌

  1. Biometrika v.68 On two families of transformations to additivity for binary response data Aranda-Ordaz, F. J.
  2. Convergence of Probability Measures Billingsley, P.
  3. Stochastic Processes and Their Applications v.27 The invariance principle for associated processes Birkel, T.
  4. Journal of Multivariate Analysis v.44 A functional central limit theorem for positively dependent random variables Birkel, T.
  5. Time Series : Theory and Methods Brockwell, P. J.;Davis, R. A.
  6. The Annals of Probability v.12 Central limit theorems for associated random variables and the percolation model Cox, J. T.;Grimmet, G.
  7. The Annals of Mathematical Statistics v.38 Association of random variables with applications Esary, J.;Proschan, F.;Walkup, D.
  8. Introduction to Statistical Time Series(2nd ed.) Fuller, W. A.
  9. Multivariate Time Series Hannan, E. J.
  10. Probability and Mathematical Statistics v.18 On the almost sure central limit theorems for associated random variables Matula, P.
  11. Inequalities in Statistics and Probability v.5 Asymptotic independence and limit theorems for positively and negatively dependent random variables Newman, C. M.
  12. The Annals of Probability v.9 An invariance principle for certain dependent sequences Newman, C. M.;Wright, A. L.
  13. Journal of Multivariate Analysis v.50 Asymptotic normality of random fields of positively of negatively associated processes Roussas, G. G.
  14. Almost Sure Convergence Stout, W. F.