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Chung type strong laws for arrays of random elements and bootstrapping. (English) Zbl 0899.60028
Summary: Let \(\{X_{nk}\}\) be an array of rowwise independent random elements in a separable Banach space. Chung type strong laws of large numbers are obtained under various moment conditions on the random elements and geometric type \(p\), \(1\leq p\leq 2\), conditions on the Banach space. Comparisons with existing results for arrays of random elements are provided to illustrate the strength of these results. The results can be directly applied to show the asymptotic validity of the bootstrap mean and variance for random functions.

60F15 Strong limit theorems
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