scholarly journals Necessary and sufficient conditions for the strong law of large numbers for U-statistics

2000 ◽  
Vol 28 (4) ◽  
pp. 1908-1924 ◽  
Author(s):  
Rafał Latała ◽  
Joel Zinn
Keyword(s):  
Law Of Large Numbers ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Strong Law ◽  
U Statistics ◽  
Large Numbers ◽  
Necessary And Sufficient

scholarly journals Weighted Strong Law of Large Numbers for Random Variables Indexed by a Sector

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Przemysław Matuła ◽  
Michał Seweryn
Keyword(s):  
Law Of Large Numbers ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Independent Random Variables ◽  
Strong Law ◽  
Large Numbers ◽  
Multidimensional Indices ◽  
Necessary And Sufficient

We find necessary and sufficient conditions for the weighted strong law of large numbers for independent random variables with multidimensional indices belonging to some sector.

Two-parameter strong laws and maximal inequalities for U-statistics

1987 ◽  
Vol 107 (1-2) ◽  
pp. 133-151 ◽  
Author(s):  
Terry R. McConnell
Keyword(s):  
Law Of Large Numbers ◽  
Weak Type ◽  
Sufficient Conditions ◽  
Strong Law ◽  
Strong Laws ◽  
Maximal Inequalities ◽  
U Statistics ◽  
Large Numbers ◽  
Necessary And Sufficient ◽  
Two Parameter

SynopsisWe provide necessary and sufficient conditions for two-parameter convergence in the strong law of large numbers for U-statistics. We also obtain weak-type (1,1) inequalities for one and two-sample U-statistics of order 2 which are, in a sense, best possible.

scholarly journals Complete Moment Convergence for Sung’s Type Weighted Sums ofB-Valued Random Elements

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Wei Li ◽  
Pingyan Chen ◽  
Soo Hak Sung
Keyword(s):  
Law Of Large Numbers ◽  
Sufficient Conditions ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Real Numbers ◽  
Strong Law ◽  
Moment Convergence ◽  
Large Numbers ◽  
Random Elements ◽  
Necessary And Sufficient

Letp≥1/αand1/2<α≤1.Let{X,Xn,  n≥1}be a sequence of independent and identically distributedB-valued random elements and let{ani,  1≤i≤n,  n≥1}be an array of real numbers satisfying∑i=1naniq=O(n)for someq>p.We give necessary and sufficient conditions for complete moment convergence of the form∑n=1∞n(p-v)α-2E∑i=1naniXi-εnα+v<∞,  ∀ε>0, where0<v<p.A strong law of large numbers for weighted sums of independentB-valued random elements is also obtained.

scholarly journals Strong laws of large numbers for the sequence of the maximum of partial sums of i.i.d. random variables

2019 ◽  
Vol 39 (1) ◽  
pp. 19-38
Author(s):  
Shuhua Chang ◽  
Deli Li ◽  
Andrew Rosalsky
Keyword(s):  
Law Of Large Numbers ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Random Variable ◽  
Partial Sums ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Necessary And Sufficient

Let 0 < p ≤ 2, let {Xn; n ≥ 1} be a sequence of independent copies of a real-valued random variable X, and set Sn = X1 + . . . + Xn, n ≥ ­ 1. Motivated by a theorem of Mikosch 1984, this note is devoted to establishing a strong law of large numbers for the sequence {max1≤k≤n |Sk| ; n ≥ ­ 1}. More specifically, necessary and sufficient conditions are given forlimn→∞ max1≤k≤n |Sk|log n−1 = e1/p a.s.,where log x = loge max{e, x}, x ≥­ 0.

A remark on strong law of large numbers for weighted U-statistics

2014 ◽  
Vol 30 (9) ◽  
pp. 1595-1605
Author(s):  
Hyung-Tae Ha ◽  
Mei Ling Huang ◽  
De Li Li
Keyword(s):  
Law Of Large Numbers ◽  
Strong Law ◽  
U Statistics ◽  
Large Numbers
Sign in / Sign up

Export Citation Format

Share Document