Let {Xk,i; i â‰¥ 1, k â‰¥ 1} be an array of i.i.d. random variables and let {pn;n â‰¥ 1} be a sequence of positive integers such that n/pn is bounded away from 0 and âˆž. For Wn = max1â‰¤i<jâ‰¤pn | âˆ‘n k=1â€¦ (More)

Let {Xk,i ; i â‰¥ 1, k â‰¥ 1} be a double array of nondegenerate i.i.d. random variables and let {pn; n â‰¥ 1} be a sequence of positive integers such that n/pn is bounded away from 0 and âˆž. In this paperâ€¦ (More)

Concentrating mainly on independent and identically distributed (i.i.d.) real-valued parent sequences, we give an overview of first-order limit theorems available for bootstrapped sample sums forâ€¦ (More)

Let {X,Xk,i; i â‰¥ 1, k â‰¥ 1} be a double array of nondegenerate i.i.d. random variables and let {pn; n â‰¥ 1} be a sequence of positive integers such that n/pn is bounded away from 0 and âˆž. This work isâ€¦ (More)

Let {X, X n ; n â‰¥ 1} be a sequence of real-valued i.i.d. random variables and let S n = n i=1 X i , n â‰¥ 1. In this paper, we study the probabilities of large deviations of the form P(S n > tn 1/p),â€¦ (More)

For a sequence of i.i.d. Banach space-valued random variables {Xn; n â‰¥ 1} and a sequence of positive constants {an; n â‰¥ 1}, the relationship between the Baumâ€“Katzâ€“Spitzer complete convergence theoremâ€¦ (More)

Let {Xn; n â‰¥ 1} be a sequence of independent copies of a real-valued random variable X and set Sn = X1 + Â· Â· Â· + Xn, n â‰¥ 1. This paper is devoted to a refinement of the classicalâ€¦ (More)

The authors in their article [2] misstated a result due to MÃ³ricz, Su, and Taylor [1]. This misstatement resulted in an invalid formulation and proof of a corollary presented in [2]. In thisâ€¦ (More)