Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables

다국어 초록 (Multilingual Abstract)

Let ｛Xnk,1 ≤ k ≤ n, n ≥ 1｝ be an array of rowwise negatively orthant dependent random variables and let fan; n ≥ 1g be a sequence of positive real numbers with an ↑∞. The convergence properties of partial sums 1an Pn k D1 Xnk are investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [Hu, T. C., Taylor R. L. (1997). On the strong law for arrays and for the bootstrap mean and variance. International Journal of Mathematics and Mathematical Sciences, 20(2), 375382].

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