鞅差序列加权和的中心极限定理

对一类鞅差序列,我们获得了其加权和中心极限定理,并给出了在非线性回归模型及线性模型中的应用。     

多维随机向量序列加权和的中心极限定理

本文研究了多维随机向量序列加权和的渐近行为.利用Lindeberg中心极限定理的基本思想,得到了多维随机向量序列加权和的中心极限定理及其收敛速度,为Lindeberg中心极限定理的推广.     

AANA随机变量序列的中心极限定理

研究了渐近几乎负相依(简称为AANA)随机变量序列的渐近正态问题.在非常一般的条件下,得到了AANA序列的中心极限定理,推广了负相依(简称为NA)、独立随机变量序列的相应结论.     

NA序列中心极限定理的收敛速度

本文对NA（NegativelyAssociated）序列建立了中心极限定理的一致收敛速度，只要其三阶矩有限及描述NA序列协方差结构的一个系数u（n）被负指数序列所控制，而无需平稳性便获得了其收敛速度O（n(-1/2)logn）。     

相依序列加权和的几乎处处中心极限定理

该文讨论了非平稳负(正)相依序列加权和的几乎处处中心极限定理,改进并推广了相依序列几乎处处中心极限定理的相关结果.     

随机变量序列函数的几乎处处中心极限定理

该文证明了随机元序列的一个一般的几乎处处中心极限定理, 并把这一结论应用于随机变量序列的函数.     

非平稳NA序列中心极限定理的一些结果

本文讨论了非平稳同分布ＮＡ序列的渐近正态问题，给出了两个中心极限定理，以往的文献在讨论ＮＡ序列的这些问题时，多加有强平稳的限制；但是大量问题所出现的ＮＡ序列却多为非平稳的，因此有开展研究的必要。本文在寻求摆脱平稳性限制的途径方面作了有益的尝试，所得的定理不仅可解决一大类非平稳ＮＡ序列的渐近正态问题，而且将以往的强平稳场合的结果包含为特例，具有一定的理论意义与应用价值。     

不同分布NA列加权和的强极限定理及其在线性模型中的应用

本文讨论了不同分布ＮＡ列Ｓｔｏｕｔ型加权和的完全收敛性和强稳定性，推广并改进了Ｓｔｏｕｔ关于ｉｉｄ列的相应结果，从而将赵林城关于独立误差的方差估计的强收敛速度的理想结果推广到ＮＡ误差的场合。     

关于任意随机适应序列部分和的一类局部极限定理

研究任意随机适应序列部分和的一类局部极限定理,推广了最近发表的几个结果．     

基于中心极限定理的信源序列的霍夫曼编码方法

借助中心极限定理,提出一种限失真霍夫曼编码方法.首先对信源扩展序列自信息量采用标准化,并定义其为标准信息量.根据中心极限定理,提出一类α-经典序列.然后将其作为编码序列进行霍夫曼编码.接着证明了α-经典序列霍夫曼编码具有较高的编码效率、较低的编码复杂度等一系列良好的性质.最后文中通过实例对扩展信源和其α-经典序列两种编码进行了比较,验证了上述结论.     

行为NSD随机变量阵列加权和的q阶矩完全收敛性

利用Hoffmann-Jφrgensen型概率不等式和截尾法,获得了行为NSD随机变量阵列加权和的q阶矩完全收敛性的充分条件.利用这些充分条件,不仅推广和深化梁汉营等(2010)和郭明乐等(2014)的结论,而且使他们的证明过程得到了极大地简化.     

A random CLT for dependent random variables

We introduce a new condition for {Y_τn} to have the same asymptotic distribution that {Y_n} has, where {Y_n} is a sequence of random elements of a metric space (S, d) and {τ_n} is a sequence of random indices. The condition on {Y_n} is that max_iDnd(Y_i, Y_an)→^p0 as n → ∞, where D_n = {i: |k_i−k_an| ≤ δ_ank_an} and {δ_n} is a nonincreasing sequence of positive numbers. The condition on {τ_n} is that P(|(k_τn/k_an)−1| > δ_an) → 0 as n → ∞. Under these conditions, we will show that d(Y_τn, Y_an) → ^P0 and apply this result to the CLT for a general class of sequences of dependent random variables.     

A central limit theorem for random sums of random variables

Anscombe (1952) (also see Chung (1974)) has developed a central limit theoremof random sums of independent and identically distributed random variables. Applicability of this theorem in practice, however, is limited since the normalization requires random factors. In this paper we establish sufficient conditions under which the central limit theorem holds when such random factors are replaced by the underlying asymptotic mean and standard ddeviation. An application of this result in the context of shock models is also given.     

On the rate of complete convergence for weighted sums of NSD random variables and an application

In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.     

Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models

We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent (WOD) random variables, which improve and extend the corresponding results of Y. F. Wu, M. G. Zhai, and J. Y. Peng [J. Math. Inequal., 2019, 13(1): 251–260]. As an application of the main results, we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.     

On the asymptotic normality of sequences of weak dependent random variables

The aim of this paper is to investigate the asymptotic normality for strong mixing sequences of random variables in the absense of stationarity or strong mixing rates. An additional condition is imposed to the coefficients of interlaced mixing. The results are applied to linear processes of strongly mixing sequences. The class of applications include filters of certain Gaussian sequences.Supported in part by an NSF grant, cost-sharing from the University of Cincinnati, and a Taft research grant.     

两两NQD列的Lp收敛性和完全收敛性

在较宽泛的条件下研究了不同分布两两NQD列加权和的收敛性质,利用矩不等式和截尾方法,获得了一般双下标加权系数的加权部分和的LP收敛性和完全收敛性定理,推广了前人的相应结果.     

Maximum of partial sums and an invariance principle for a class of weak dependent random variables

The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle and the convergence of the moments in the central limit theorem.

     

A note on rates of convergence in the multidimensional CLT for maximum partial sums

In this note we obtain rates of convergence in the central limit theorem for certain maximum of coordinate partial sums of independent identically distributed random vectors having positive mean vector and a nonsingular correlation matrix. The results obtained are in terms of rates of convergence in the multidimensional central limit theorem. Thus under the conditions of Sazonov (1968, Sankhya, Series A30 181–204, Theorem 2), we have the same rate of convergence for the vector of coordinate maximums. Other conditions for the multidimensional CLT are also discussed, c.f., Bhattachaya (1977, Ann. Probability 5 1–27). As an application of one of the results we obtain a multivariate extension of a theorem of Rogozin (1966, Theor. Probability Appl. 11 438–441).