×

zbMATH — the first resource for mathematics

On strong laws of large numbers for arrays of rowwise independent random elements. (English) Zbl 0844.60005
Summary: Let \(\{X_{nk}\}\) be an array of rowwise independent random elements in a separable Banach space of type \(r\), \(1 \leq r \leq 2\). Complete convergence of \(n^{1/p} \sum^n_{k = 1} X_{nk}\) to 0, \(0 < p < r \leq 2\), is obtained when \(\sup_{1 \leq k \leq n} E|X_{nk}|^\nu = O(n^\alpha)\), \(\alpha \geq 0\), with \(\nu(1/p - 1/r) > \alpha + 1\). An application to density estimation is also given.

MSC:
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
62G05 Nonparametric estimation
60F15 Strong limit theorems
PDF BibTeX Cite
Full Text: DOI Link EuDML