Almost Sure lim sup Behavior of Dependent Bootstrap Means

REFERENCES

• Efron , B. 1979 . Bootstrap methods: Another look at the jackknife . Ann Statist. 7 : 1 – 26 . [CSA]
   Web of Science ®Google Scholar
• Athreya , K.B. 1983 . Strong law for the bootstrap . Statist. Probab. Lett. 1 : 147 – 150 . [CSA] [CROSSREF]
   Google Scholar
• Csörgö , S. 1992 . On the law of large numbers for the bootstrap mean . Statist. Probab. Lett. 14 : 1 – 7 [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Arenal-Gutiérrez , E. , C. Matrán , and J.A. Cuesta-Albertos . 1996 . On the unconditional strong law of large numbers for the bootstrap mean . Statist. Probab. Lett. 27 : 49 – 60 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Mikosch , T. 1994 . Almost sure convergence of bootstrapped means and U-statistics . J. Statist. Plann. Inference 41 : 1 – 19 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Ahmed , S.E. , D. Li , A. Rosalsky , and A. Volodin . 2001 . Almost sure lim sup behavior of bootstrapped means with applications to pairwise i.i.d. sequences and stationary ergodic sequences . J. Statist. Plann. Inference 98 : 1 – 14 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Smith , W. , and R.L. Taylor . 2001. Consistency of dependent bootstrap estimators. American Journal of Mathematics and Management Sciences 21(3&4):359–382. [CSA]
   Google Scholar
• Smith , W. , and R.L. Taylor . 2001 . Dependent bootstrap confidence intervals . Selected Proceedings of the Symposium on Inference for Stochastic Processes . IMS Lecture Notes—Monograph Series 37 : 91 – 107 .
   Google Scholar
• Lehmann , E. 1966 . Some concepts of dependence . Ann. Math. Statist. 37 : 1137 – 1153 . [CSA]
   Google Scholar
• Taylor , R.L. , P. Daffer , and R. Patterson . 1985 . Limit Theorems for Sums of Exchangeable Random Variables . Rowman & Allanheld Probability and Statistics Series . Totowa , NJ : Rowman & Allanheld, Publishers .
   Google Scholar
• Bozorgnia , A. , R.F. Patterson , and R.L. Taylor . 1996 . Limit therorms for dependent random variables . In: Proceedings of the WCNA'92 . pp. 1639 – 1650 . Florida : Tampa .
   Google Scholar
• Barnes , G. , and H. Tucker . 1977 . On almost sure convergence of normed maxima of independent random variables . J. London Math. Soc. 16 ( 2 ): 377 – 383 . [CSA]
   Google Scholar
• Stout , W.F. 1974 . Almost Sure Convergence . New York : Academic Press .
   Google Scholar
• Volodin , A. 2002 . On the Kolmogorov exponential inequality for negatively dependent random variables . Pakistan J. Statist. 18 : 249 – 253 . [CSA]
   Google Scholar
• Etemadi , N. 1981 . An elementary proof of the strong law of large numbers . Z. Wahrsch. Verw. Gebiete 55 : 119 – 122 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bickel , P.J. , and D.A. Freedman . 1981 . Some asymptotic theory for the bootstrap . Ann. Statist. 9 : 1196 – 1217 . [CSA]
   Web of Science ®Google Scholar