Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables

In this paper,the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated.Some sufficient conditions for the convergence are provided.In addition,the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables is obtained.The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables.     

Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables

In this paper, complete moment convergence for widely orthant dependent random variables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.     

一般矩条件下相依随机变量Sung型加权和的完全收敛性

在一般矩条件下,本文得到了END随机变量和PNQD随机变量的Sung型加权和的完全收敛性定理,这些定理推广了已知的一些文献中相应的结果.     

NOD随机变量随机加权部分和的完全收敛性

本文研究了NOD随机变量双下标随机加权部分和的完全收敛性,获得了一些完全矩收敛结果和完全收敛结果,从而获得了Marcinkiewicz-Zygmund型强大数律.我们的结果推广了目前已有的一些结论.进一步,我们给出一些数据模拟工作来展示收敛性结果.     

Equivalent Conditions of Complete qth Moment Convergence for Weighted Sums of Sequences of Negatively Orthant Dependent Random Variables

In this paper, the complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables are established. These results not only extend the corresponding results obtained by Li and Sp\v{a}taru\ucite{4}, Liang et al.\ucite{5}, Guo\ucite{6} and Gut\ucite{21} to sequences of negatively orthant dependent random variables, but also improve them.     

Complete Convergence of Weighted Sums for Arrays of Rowwise $m$-Negatively Associated Random Variables

In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise $m$-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise $m$-negatively associated random variables are established. These results generalize and complement some known conclusions.     

Complete Convergence of Weighted Sums for Arrays of Rowwise m-negatively Asso ciated Random Variables

In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions.     

Complete moment convergence for arrays of rowwise NSD random variables

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.     

行内负相关随机变量组列的完全收敛性

运用NA随机变量的矩不等式以及邵启满给出的关于NA随机变量概率不等式,在NA的情况下给出了类似与Chen(2005),Sung(2005)关于行内独立随机变量完全收敛性的结论.同时在给出的条件比上述作者的结论条件更加弱.     

Exponential Inequalities and Complete Convergence for Extended Negatively Dependent Random Variables

Some exponential inequalities and complete convergence are established for extended negatively dependent（END） random variables. The inequalities extend and improve the results of Kim and Kim（On the exponential inequality for negative dependent sequence. Communications of the Korean Mathematical Society, 2007, 22（2）： 315-321） and Nooghabi and Azarnoosh（Exponential inequality for negatively associated random variables. Statisti- cal Papers, 2009, 50 （2）： 419-428）. We also obtain the convergence rate O（n-1/2 In1/2 n） for the strong law of large numbers, which improves the corresponding ones of Kim and Kim, and Nooghabi and Azarnoosh.     

Complete f-moment Convergence for Widely Orthant Dependent Random Variables and Its Application in Nonparametric Models

In this paper, we study the complete f-moment convergence for widely orthant dependent (WOD, for short) random variables. A general result on complete f-moment convergence for arrays of rowwise WOD random variables is obtained. As applications, we present some new results on complete f-moment convergence for WOD random variables. We also give an application to nonparametric regression models based on WOD errors by using the complete convergence that we established. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed, and a numerical simulation is provided to verify the validity of the theoretical result.     

Complete Convergence for Weighted Sums of Arrays of Rowwise Asymptotically Almost Negative Associated Random Variables

Let be an array of rowwise asymptotically almost negative associated (AANA, in short) random variables. The complete convergence for weighted sums of arrays of rowwise AANA random variables is established under some general moment conditions. The result obtained in the paper generalizes and improves the corresponding one for negatively associated random variables.     

Complete Convergence for Weighted Sums of Negatively Sup eradditive Dep endent Random Variables

In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some su?cient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables.     

END随机变量的概率不等式及其应用(英文)

Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results.     

Complete Convergence for Weighted Sums of WOD Random Variables

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent ran-dom variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.     

不同分布NA序列加权和的完全收敛性

本文讨论了不同分布NA随机变量序列加权和的完全收敛性，获得了较[7]中的定理1及定理A更为一般的安全收敛性，并得到了完全收敛速度与矩条件之间的等价关系。     

相依随机变量阵列加权和的矩完全收敛性

本文研究了相依随机变量阵列加权和的矩完全收敛性.利用矩不等式和截尾法,建立了相依随机变量阵列加权和的矩完全收敛性的充分条件.将Volodin等(2004)及陈平炎等(2006)的关于独立随机变量阵列的结果推广到了负相协和负相依随机变量阵列的情形,推广并完善了Sung(2011),吴群英(2012)及郭明乐和祝东进(2012)的结果.     

Moment Complete Convergence for Weighted Sums of -Mixing Random Variables

In this paper, the authors discuss the moment complete convergence for weighted sums of -mixing random variables, and obtains the sufficient condition for moment complete convergence of -mixing sequence under some mixing rate condition, which generalize the result of moment complete convergence for weighted sums of i.i.d. random variables to -mixing random variables.     

行为ND随机变量阵列加权和的完全收敛性

在非同分布的情况下,给出了行为ND随机变量阵列加权和的完全收敛性的充分条件,所得结果部分地推广了独立随机变量和NA随机变量的相应结果.作为其应用,获得了ND随机变量序列加权和的Marcinkiewicz-Zygmund型强大数定律.     

NA随机变量阵列加权和的矩完全收敛性

In this paper we obtain some new results on complete moment convergence for weighted sums of arrays of rowwise NA random variables.Our results improve and extend some well known results from the litera...