• Communications for Statistical Applications and Methods
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• 제1권1호
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• pp.149-156
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• 1994

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.

• 대한수학회지
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• 제37권3호
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• pp.463-471
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• 2000

A central limit theorem is obtained for stationary linear process Xt = aj$\varepsilon$t-j, where {$\varepsilon$t} a strictly stationary associated sequence with Et < and {aj} is a sequence of real numbers with <. A functional central limit theorem is also derived.

• 대한수학회논문집
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• 제26권1호
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• pp.151-161
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• 2011

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

• Journal of the Korean Statistical Society
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• 제31권3호
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• pp.369-378
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• 2002

Strong laws of large numbers for weighted sums of asymptotically almost negatively associated(AANA) sequence are proved by our generalized maximal inequality for AANA random variables at a crucial step.

• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.615-623
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• 2001

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).).