Almost Sure lim sup Behavior of Dependent Bootstrap Means

Abstract

In this article, the upper bound for the exact convergence rate (i.e., the law of the logarithm type result) is obtained for dependent bootstrap means.

Keywords:

• Bootstrap means
• Dependent bootstrap
• Kolmogorov exponential inequality
• Law of the logarithm
• Pairwise i.i.d. sequences
• Stationary ergodic sequences

Mathematics Subject Classification:

• Primary 62E20, 62G05
• Secondary 60F15

ACKNOWLEDGMENTS

The work of A. Volodin is supported by a grant from the National Sciences and Engineering Research Council of Canada. The work of M. Ordóñez Cabrera is supported by grants BFM 2000-0344-C0201 and FQM 127. The work of T.-C. Hu is supported by the grant NSC91-2118-M-007-008. The authors are exceptionally grateful to the referee for offering helpful remarks and comments that improved presentation of the paper.