Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Maximal Inequality for Partial Sums of Negatively Associated Sequences

  • Tae Sung Kim (Department of Statistics, Won-Kwang University, Iri(570-749), KOREA) ;
  • Hye Young Seo (Department of Statistics, Won-Kwang University, Iri(570-749), KOREA) ;
  • In Bong Choi (Department of Statistics, Won-Kwang University, Iri(570-749), KOREA)
  • Published : 1994.12.01
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Abstract

For an r > 2 and a finite B, $E\mid max \;1\leq k\leq n \;\sum\limits_{j=m+1}^{m+k}X_j\mid^r\leq Bn^ {\frac{r}{2}}$ (all $n\geq 1$) is obtained for a negatively associated sequence $\{X_j \;:\; j\in N\}$. We also derive the maximal inequelity for a negatively associated sequence. Stationarity is not required.

Keywords

References

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  3. The Annals of Mathematical Statistics v.38 Association of random variables with application Esary, J.;Prochan, F.;Walkup, D.
  4. The Annals of Statistics v.11 Negative association of random variables, with applications Joag-Dev, K.;Proschan, F.
  5. Inequalities in Statistics and Probability IMS Lecture Notes, Monograph Series v.5 Asymptotic independent and limits theorems for positively and negatively dependent random variables Newman, C. M.
  6. Almost sure Convergence Stout, W.