On the strong law for arrays and for the bootstrap mean and variance. (English) Zbl 0883.60024

The strong law of large numbers for a triangular array \(\{X_{ni}\), \(1\leq i \leq n, n\geq 1\}\) of row-wise independent (but neither necessarily identically distributed nor independent between rows) random variables is established under conditions similar to those of Chung. Further this result is related to verifying a known fact of consistency of the bootstrap mean and bootstrap variance [cf. S. C\"sorgö, Stat. Probab. Lett. 14, No. 1, 1-7 (1992; Zbl 0752.62034)]. The authors present a new, fairly different approach to this problem in a natural formulation. Let us mention that in Theorem 2.1 not only a.s. but even complete convergence can be stated.


60F15 Strong limit theorems
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)


Zbl 0752.62034
Full Text: DOI EuDML