scholarly journals Precise asymptotics for complete moment convergence of U-statistics of i.i.d. random variables

2012 ◽  
Vol 25 (2) ◽  
pp. 120-127 ◽  
Author(s):  
Qing-pei Zang
Keyword(s):  
Random Variables ◽  
Complete Moment Convergence ◽  
Precise Asymptotics ◽  
Moment Convergence

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.

scholarly journals Complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1093-1104
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Probability Space ◽  
Complete Convergence ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables

This paper we study and establish the complete convergence and complete moment convergence theorems under a sub-linear expectation space. As applications, the complete convergence and complete moment convergence for negatively dependent random variables with CV (exp (ln? |X|)) < ?, ? > 1 have been generalized to the sub-linear expectation space context. We extend some complete convergence and complete moment convergence theorems for the traditional probability space to the sub-linear expectation space. Our results generalize corresponding results obtained by Gut and Stadtm?ller (2011), Qiu and Chen (2014) and Wu and Jiang (2016). There is no report on the complete moment convergence under sub-linear expectation, and we provide the method to study this subject.

Complete moment convergence forweighted sums of pairwise negatively quadrant dependent random variables

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3459-3471
Author(s):  
Mingming Zhao ◽  
Shengnan Ding ◽  
Di Zhang ◽  
Xuejun Wang
Keyword(s):  
Theoretical Result ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Dependent Random Variables ◽  
Moment Convergence

In this article, the complete moment convergence for weighted sums of pairwise negatively quadrant dependent (NQD, for short) random variables is studied. Several sufficient conditions to prove the complete moment convergence for weighted sums of NQD random variables are presented. The results obtained in the paper extend some corresponding ones in the literature. The simulation is also presented which can verify the validity of the theoretical result.

scholarly journals Precise Asymptotics for Complete Integral Convergence under Sublinear Expectations

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Complete Moment Convergence ◽  
Precise Asymptotics ◽  
Convergence Theorems ◽  
Sublinear Expectation ◽  
Moment Convergence

The aim of this paper is to study and establish the precise asymptotics for complete integral convergence theorems under a sublinear expectation space. As applications, the precise asymptotics for p0≤p≤2 order complete integral convergence theorems have been generalized to the sublinear expectation space context. We extend some precise asymptotics for complete moment convergence theorems from the traditional probability space to the sublinear expectation space. Our results generalize corresponding results obtained by Liu and Lin (2006). There is no report on the precise asymptotics under sublinear expectation, and we provide the method to study this subject.

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