Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process

2008 ◽  
Vol 78 (9) ◽  
pp. 1051-1055 ◽  
Author(s):  
Yong Zhang ◽  
Xiao-Yun Yang
Keyword(s):  
Complete Convergence ◽  
Empirical Process ◽  
Precise Asymptotics ◽  
Iterated Logarithm ◽  
The Law ◽  
Uniform Empirical Process

scholarly journals Precise Asymptotics in the Law of the Iterated Logarithm under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mingzhou Xu ◽  
Kun Cheng
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Uniform Convergence ◽  
Central Limit ◽  
Random Variables ◽  
Precise Asymptotics ◽  
Partial Sum ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

By an inequality of partial sum and uniform convergence of the central limit theorem under sublinear expectations, we establish precise asymptotics in the law of the iterated logarithm for independent and identically distributed random variables under sublinear expectations.

scholarly journals Precise asymptotics in the law of the iterated logarithm

2000 ◽  
Vol 28 (4) ◽  
pp. 1870-1883 ◽  
Author(s):  
Allan Gut ◽  
Aurel Spătaru
Keyword(s):  
Precise Asymptotics ◽  
Iterated Logarithm ◽  
The Law

scholarly journals Precise asymptotics in the law of the iterated logarithm for R/S statistic

2014 ◽  
Vol 2014 (1) ◽  
pp. 137
Author(s):  
Tian-Xiao Pang ◽  
Zheng-Yan Lin ◽  
Kyo-Shin Hwang
Keyword(s):  
Precise Asymptotics ◽  
Iterated Logarithm ◽  
The Law

scholarly journals Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Junshan Xie ◽  
Lin He
Keyword(s):  
Empirical Process ◽  
Random Variables ◽  
Nonnegative Function ◽  
Second Order ◽  
Complete Moment Convergence ◽  
Precise Asymptotics ◽  
Moment Convergence ◽  
Uniform Empirical Process

Let{ξi,1≤i≤n}be a sequence of iidU[0, 1]-distributed random variables, and define the uniform empirical processFn(t)=n-1/2∑i=1n‍(I{ξi≤t}-t),0≤t≤1,Fn=sup0≤t≤1|Fn(t)|. When the nonnegative functiong(x)satisfies some regular monotone conditions, it proves thatlimϵ↘0⁡1/-logϵ∑n=1∞g′(n)/g(n)E{Fn2I{∥Fn∥≥ϵg(n)}}=π2/6.

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