负相协随机变量的指数不等式

该文给出了一些负相协随机变量的指数不等式.这些不等式改进了由Jabbari和Azarnoosh^[4]及Oliveira^[7] 所得到的相应的结果.利用这些不等式对协方差系数为几何下降情形, 获得了强大数律的收敛速度为n^-1/2(log log n)^1/2(log n)^2.这个收敛速度接近独立随机变量的重对数律的收敛速度, 而Jabbari和Azarnoosh^[4]在上述情形下得到的收敛速度仅仅为n^-1/3(log n)^5/3.     

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.     

Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm

Kolmogorov’s exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments. For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sub-linear expectation for random variables with only finite variances.     

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.     

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.     

负相关随机变量序列的对数律

在本文中,首先我们得到了负相关(ND)随机变量序列的指数不等式和矩不等式,然后运用这些不等式讨论了ND序列的对数律.结果,我们将独立情形下的对数律推广到ND序列情形下依然成立.     

On the exponential inequalities for negatively dependent random variables

A number of exponential inequalities for identically distributed negatively dependent and negatively associated random variables have been established by many authors. The proofs use the truncation technique together with the control of the bounded terms and unbounded terms. In this paper, we improve essentially the control of bounds for the unbounded terms and obtain exponential inequalities for negatively dependent random variables which include negatively associated random variables. Our results improve on the corresponding ones in the literature.     

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本文给出了上期望空间中独立随机变量部分和的最大不等式、指数 不等式、Marcinkiewicz-Zygmund不等式. 并且应用指数不等式和Marcinkiewicz-Zygmund不等式 研究了随机变量部分和序列完备收敛的性质.     

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent (NSD, in short) random variables is established. By using the exponential inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.     

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.     

NSD变量加权和的完全收敛性（英文）

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 sufficient 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.     

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.     

Almost sure convergence theorem and strong stability for weighted sums of NSD random variables

In this paper, Kolmogorov-type inequality for negatively superadditive dependent (NSD) random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated (NA) sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.     

Exponential inequalities for associated random variables and strong laws of large numbers

Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.     

Asymptotic Property of <Emphasis Type="Italic">M</Emphasis> Estimator in Classical Linear Models Under Dependent Random Errors

In this paper, we first establish a useful result on strong convergence for weighted sums of widely orthant dependent (WOD, in short) random variables. Based on the strong convergence that we established and the Bernstein type inequality, we investigate the strong consistency of M estimators of the regression parameters in linear models based on WOD random errors under some more mild moment conditions. The results obtained in the paper improve and extend the corresponding ones for negatively orthant dependent random variables and negatively superadditive dependent random variables. Finally, the simulation study is provided to illustrate the feasibility of the theoretical result that we established.     

Complete Convergence for Weighted Sums of Negatively Superadditive Dependent Random Variables

Let $\{X_n,n\geq1\}$ be a sequence of negatively superadditive dependent (NSD, in short) random variables and $\{a_{nk}, 1\leq k\leq n, n\geq1\}$ be an array of real numbers. Under some suitable conditions, we present some results on complete convergence for weighted sums $\sum_{k=1}^na_{nk}X_k$ of NSD random variables by using the Rosenthal type inequality. The results obtained in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.     

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.     

Exponential inequalities and inverse moment for NOD sequence

Some exponential inequalities for a negatively orthant dependent sequence are obtained. By using the exponential inequalities, we study the asymptotic approximation of inverse moment for negatively orthant dependent random variables, which generalizes and improves the corresponding results of Kaluszka and Okolewski [Kaluszka, M., Okolewski, A., 2004. On Fatou-type lemma for monotone moments of weakly convergent random variables. Statist. Probab. Lett. 66, 45–50], Hu et al. [Hu, S.H., Chen, G.J., Wang, X.J., Chen, E.B., 2007. On inverse moments of nonnegative weakly convergent random variables. Acta Math. Appl. Sin. 30, 361–367(in Chinese)] and Wu et al. [Wu, T.J., Shi, X.P., Miao, B.Q., 2009. Asymptotic approximation of inverse moments of nonnegative random variables. Statist. Probab. Lett. 79, 1366–1371].     

Some Exponential Inequalities for Negatively Orthant Dependent Random Variables

Acta Mathematicae Applicatae Sinica, English Series - In the paper, we establish some exponential inequalities for non-identically distributed negatively orthant dependent (NOD, for short) random...