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A survey of limit laws for bootstrapped sums
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 forExpand
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Some general strong laws for weighted sums of stochastically dominated random variables
For weighted sums, general strong laws of large numbers of the form almost certainly are established where the random variables are stochastically dominated by a random variable are suitableExpand
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Strong laws of large numbers for weighted sums of random elements in normed linear spaces
Consider a sequence of independent random elements {Vn, n > in a real separable normed linear space (assumed to be a Banach space in most of the results), and sequences of con-
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Strong and Weak Laws of Large Numbers for Double Sums of Independent Random Elements in Rademacher Type p Banach Spaces
Abstract For a double array of independent random elements {V mn , m ≥ 1, n ≥ 1} in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space, strong and weak laws of large numbers are establishedExpand
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On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix
TLDR
This paper is devoted to the solution to an open problem posed in Li et al. (2010) [9] on the asymptotic distribution of the largest entry L"n=max"1"@?"i" ~n^[email protected]!"("n"l"o"g"n"). Expand
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On complete convergence for arrays of rowwise independent random elements in banach spaces
We extend and generalize some recent results on complete convergence (cf. Hu, Moricz, and Taylor [14], Gut [11], Wang, Bhaskara Rao, and Yang [26], Kuczmaszewska and Szynal [17], and Sung [23]) forExpand
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A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces
For weighted sums of the form Sn = [summation operator]j=1kn anj(Vnj - cnj) where {anj, 1[less-than-or-equals, slant]j[less-than-or-equals, slant]kn
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Some Strong Laws of Large Numbers for Banach Space Valued Summands Irrespective of Their Joint Distributions
Conditions are provided under which a sequence of random elements in a real separable Banach space obeys a general strong law of large numbers. No conditions are imposed on the joint distributions ofExpand
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Laws of Large Numbers
  • A. Rosalsky
  • Mathematics, Computer Science
  • International Encyclopedia of Statistical Science
  • 2011
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Some strong limit theorems for the largest entries of sample correlation matrices
Let $\{X_{k,i};i\geq 1,k\geq 1\}$ be an array of i.i.d. random variables and let $\{p_n;n\geq 1\}$ be a sequence of positive integers such that $n/p_n$ is bounded away from 0 and $\infty$. ForExpand
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