LIMIT THEOREMS FOR SUMS AND MAXIMA OF MIRWISE NEGATIVE QUADRANT DEPENDENT RANDOM VARIABLES

ＬＩＭＩＴＴＨＥＯＲＥＭＳＦＯＲＳＵＭＳＡＮＤＭＡＸＩＭＡＯＦＭＩＲＷＩＳＥＮＥＧＡＴＩＶＥＱＵＡＤＲＡＮＴＤＥＰＥＮＤＥＮＴＲＡＮＤＯＭＶＡＲＩＡＢＬＥＳ￥ＱＩＹｏｎｇｃｈｅｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ａｃａｄｅｍｉａ...     

Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END, for short) random variables. Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided. In particular, the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product. The results that the authors obtained generalize the corresponding ones for independent ra...     

Chover’s law of the iterated logarithm for negatively associated sequences

<正> Consider a sequence of negatively associated and identically distributed random variableswith the underlying distribution in the domain of attraction of a stable distribution with an exponentin(0,2).A Chover's law of the iterated logarithm is established for negatively associated randomvariables.Our results generalize and improve those on Chover's law of the iterated logarithm(LIL)type behavior previously obtained by Mikosch(1984),Vasudeva(1984),and Qi and Cheng(1996)fromthe i.i.d,case to NA sequences.     

系统的平均有效性的极限状态

有效性是系统的一个重要性质． 本文对混合随机变量序列,证明了两种不同的平均有效性收敛到同一极限．     

Identification of Errors-in-Variables Systems with General Nonlinear Output Observations and with ARMA Observation Noises

This paper concerns the identification problem of scalar errors-in-variables(EIV) systems with general nonlinear output observations and ARMA observation noises. Under independent and identically distributed(i.i.d.) Gaussian inputs with unknown variance, recursive algorithms for estimating the parameters of the EIV systems are presented. For general nonlinear observations, conditions on the system are imposed to guarantee the almost sure convergence of the estimates. A simulation example is included to justify the theoretical results.     

Finite-time ruin probability with NQD dominated varying-tailed claims and NLOD inter-arrival times

In 2007, Chen and Ng investigated infinite-time ruin probability with constant interest force and negatively quadrant dependent and extended regularly varying-tailed claims. Following this work, the authors obtain a weakly asymptotic equivalent formula for the finite-time and infinite-time ruin probability with constant interest force, negatively quadrant dependent, and dominated varying-tailed claims and negatively lower orthant dependent inter-arrival times. In particular, when the claims are consistently varying-tailed, an asymptotic equivalent formula is presented. This research is supported by the National Science Foundation of China under Grant No. 10671139.     

LOCAL ASYMPTOTIC PROPERTIES OF HAZARD RATE ESTIMATORS FOR TRUNCATED AND CENSORED DATA

1 IntroductionLet (X, T, Y) denote random variables where X is the variab1e of interest, called the lifetimevariab1e, with distribution function (d.f.) F; T is the random 1eft truncation time with arbitraryd.f G and Y is the random right censoring time with arbitrary d.f. H. It is assumed that Xis independent Of (T, Y), bnt T and Y may be dePendent and, Without 1oss of generality thatthey are nonnegative. In the random 1eft truncation and right censoring (LTRC) model oneobserves (Z, T…     

Feature Screening for High-Dimensional Survival Data via Censored Quantile Correlation

This paper proposes a new sure independence screening procedure for high-dimensional survival data based on censored quantile correlation (CQC). This framework has two distinctive features: 1) Via incorporating a weighting scheme, our metric is a natural extension of quantile correlation (QC), considered by Li (2015), to handle high-dimensional survival data; 2) The proposed method not only is robust against outliers, but also can discover the nonlinear relationship between independent variables and censored dependent variable. Additionally, the proposed method enjoys the sure screening property under certain technical conditions. Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors.

     

Convergence in Distribution for Uncertain Random Sequences with Dependent Random Variables

Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and uncertain variables, uncertain random variable is introduced as a tool to deal with complex phenomena including randomness and uncertainty simultaneously. For uncertain random variables, a basic and important topic is to discuss the convergence of its sequence.Specifically, this paper focuses on studying the convergence in distribution for a sequence of uncertain random sequences with different chance distributions where random variables are not independent.And the result of this paper is a generalization of the existing literature. Relations among convergence theorems are studied. Furthermore, the theorems are explained by several examples.     

The limit theorem for dependent random variables with applications to autoregression models

This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {X _t } be a linear process defined by X _t = Σ _k=0^∞ψ _k ɛ _t−k , where {ψ _k , k ≥ 0} is a sequence of real numbers and {ɛ _k , k = 0, ±1, ±2, …} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {ɛ _k , k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter α when {ɛ _k , k ≥ 1} is a sequence of negatively associated (NA) random variables, and ψ ₀ = 1, ψ _k = 0, k ≥ 1.     

OPTIMAL GLOBAL RATES OF CONVERGENCE OF M－ESTIMATES FOR NONPARAMETRIC REGRESSION

ＯＰＴＩＭＡＬＧＬＯＢＡＬＲＡＴＥＳＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＭ－ＥＳＴＩＭＡＴＥＳＦＯＲＮＯＮＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＳＨＩＰｅｉｄｅ；ＬＩＧｕｏｙｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉ...     

Integral-type tests for goodness-of-fit

<正> A family of integral-type goodness-of-fit tests is investigated.This family includes someexisting tests,such as the Cramér-von Mises test and Anderson-Darling test,etc.The asymptoticdistributions of the tests in the family under the null and local alternative hypotheses are established.The almost sure convergence under a fixed underlying distribution is obtained.Furthermore,simulationsare conducted to compare the powers of the tests in the family.Simulation results show that fordifferent alternatives,the more powerful tests are different,and the parameter λ has great influence onthe tests in small sample cases.     

H∞鲁棒控制下动态供应链系统牛鞭效应优化

为解决网络化制造(networked manufacturing,NM)模式下供应链系统运作中存在的不确定性扰动, 运用H_∞鲁棒控制方法抑制供应链系统牛鞭效应, 保障系统稳定运作.构建了由状态变量和控制变量描述的NM模式下的动态供应链时变偏差系统模型,采用线性矩阵不等式(LMI)方法获取H_∞鲁棒控制策略,并通过系统反馈控制器u_k设计,有效减小客户不确定需求引起的生产、订货和库存波动. 最后,结合实例分析表明在抑制率为ζ时,本文提出的鲁棒控制策略可以有效抑制不同形式客户需求引起的牛鞭效应,实现供应链系统鲁棒镇定.     

Ruin probabilities with pairwise quasi-asymptotically independent and dominatedly-varying tailed claims

This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails.The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities.In particular,if the claims are identically distributed and consistently-varying tailed,then an asymptotic formula is presented.     

Distributed Nonsmooth Convex Optimization over Markovian Switching Random Networks with Two Step-Sizes

This paper investigates the distributed convex optimization problem over a multi-agent system with Markovian switching communication networks. The objective function is the sum of each agent's local nonsmooth objective function, which cannot be known by other agents. The communication network is assumed to switch over a set of weight-balanced directed graphs with a Markovian property. The authors propose a consensus sub-gradient algorithm with two time-scale step-sizes to handle the Markovian switching topologies and the absence of global gradient information. With proper selection of step-sizes, the authors prove the almost sure convergence of all agents' local estimates to the same optimal solution when the union graph of the Markovian network' states is strongly connected and the Markovian chain is irreducible. The convergence rate analysis is also given for specific cases.Simulations are given to demonstrate the results.     

EM算法在Wiener过程随机参数的超参数值估计中的应用

Wiener过程广泛用于产品的性能退化建模,为了便于Bayesian统计推断大都采用随机参数的共轭先验分布。针对目前的二步法得到的超参数先验估计值精度不高的问题,研究了最大期望(expectation maximization,EM)算法在Wiener过程超参数先验估计中的应用。EM算法将随机参数作为隐含变量对先验信息进行整体处理,利用随机参数的期望值代替其估计值,通过Expectation和Maximization组成的递归迭代过程寻找超参数的估计值。仿真实验表明,EM算法相比于二步法提高了估计精度,特别是在采样数量较少时EM算法具有较大的精度优势。GaAs激光器实例应用表明EM算法不但具备很好的收敛性而且有良好的工程应用价值。     

基于差分进化邻域自适应的大规模多目标算法

对于大规模决策变量给求解大规模多目标优化问题带来的难以收敛及解集分布不均匀问题,通过分析变量特征将其分类再分别优化是当前较为有效的求解方法,但存在变量分类不够准确、变量处理不够有针对性等不足。对此,提出一种基于差分进化邻域自适应策略的大规模多目标优化算法。首先,通过分析扰动解的支配关系将混合变量分为多样性变量和收敛性变量,使变量分类更为准确。其次,通过对收敛性变量主成分分析降噪,降低计算成本,并设计种群的交替进化策略及差分进化的邻域自适应更新操作以提升种群进化过程中的收敛性。实验结果表明,所提算法在收敛速度和解集的分布均匀性上表现出良好的性能。     

带丢包和量化的参数不确定系统滚动时域估计

针对网络化系统中丢包、量化和参数不确定性对状态估计的影响,提出一种带有预测补偿机制的鲁棒滚动时域估计算法。将丢包现象描述为概率已知的随机Bernoulli序列,并利用丢失数据的预测值进行丢包补偿,将数据量化引入的量化误差描述为观测方程中的一个有界不确定参数,将模型的不确定性描述为系统矩阵受到随机扰动,基于滚动优化策略,考虑量化和模型不确定性影响最严重的情况,通过滚动求解一个min-max问题得到最优状态估计器。对所提算法进行稳定性分析,推导了估计误差范数平方期望的一个上界函数,给出了估计误差范数平方期望收敛的充分条件。最后,通过仿真验证了所提算法的有效性。     

End-to-end rate-based congestion control with random loss: convergence and stability

The convergence and stability analysis for two end-to-end rate-based congestion control algorithms with unavoidable random loss in packets are presented, which can be caused by, for example, errors on wireless links. The convergence rates of these two algorithms are analyzed by linearizing them around their equilibrium points, since they are globally stable and can converge to their unique equilibrium points. Some sufficient conditions for local stability in the presence of round-trip delay are obtained based on the general Nyquist criterion of stability. The stability conditions can be considered to be more general. If random loss in the first congestion control algorithm is not considered, they reduce to the local stability conditions which have been obtained in some literatures. Furthermore, sufficient conditions for local stability of a new congestion control algorithm have also been obtained if random loss is not considered in the second congestion control algorithm.     

Approach to stochastic multi-attribute decision problems using rough sets theory

1.INTRODUCTIONMulti-attribute decision making(MADM)is widely ap-pliedin manyfields such as military affairs,economy andmanagement.When dealing with MADM,it is usual tobe confrontedtoa context of uncertainty.This uncertain-tycan originate fromdifferent sources[1].We suppose inthis paper that uncertaintyis due to the fact that perfor-mance evaluations of alternatives on each of the attributeslead to random variables with probability distribution.This kind of problems are called stochasti…