zbMATH — the first resource for mathematics

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.

MSC:
 60F15 Strong limit theorems
Full Text:
References:
 [1] Adler A., Bull. Inst. Math.,Academia Sinica 20 pp 335– (1992) [2] DOI: 10.1016/0378-3758(84)90019-3 · Zbl 0533.62043 [3] Beck A., Ergodic Theory pp 21– (1963) [4] DOI: 10.1214/aos/1176345637 · Zbl 0449.62034 [5] DOI: 10.1155/S0161171293000729 · Zbl 0844.60005 [6] DOI: 10.2307/2371664 · Zbl 0034.07103 [7] DOI: 10.1214/aop/1176996029 · Zbl 0368.60022 [8] Hu T.C., On the strong law for arrays and for the bootstrap mean and variance (1995) [9] Marcinkiewicz J., Fund.Math 29 pp 60– (1937) [10] Mourier E., Ann.Inst Henri Poincare 13 pp 159– (1953) [11] Stein E., Singular Integrals and Differentiability Properties of Functions (1970) · Zbl 0207.13501 [12] Taylor R.L., Lecture Notes in Mathematics 672 (1978) [13] DOI: 10.1155/S0161171287000899 · Zbl 0628.60011 [14] Woyczynski W.A., Advances in Probability 4 pp 267– (1978) [15] Woyczynski W.A., Prob.and Math.Stat 1 pp 117– (1980)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.