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本文主要讨论了变点的先验分布为beta-binomial分布 和Ibrahim等(2003)提出的幂型先验的条件下, 有一个变点的线性模型的贝叶斯统计推断问题, 并且我们假定变点两边的观测值的方差是相等的. 我们得到变点、回归系数、共同方差的后要分布的显示表达式. 本论文不仅把Ferrira(1975)论文从变点先验分布服从离散均匀分布推广到了更好描述变点 的形状的beta-binomial分布, 而且进一步将变点的先验分布推广到包含的历史信息的幂型先验. 当变点的先验分布为beta-binomial分布和幂型先验时, 模拟结果显示了贝叶斯方法具有更高的准确性.     

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本文研究了独立随机变量之和的绝对矩的几个性质, 其中包括$\ep|X+Y|-\ep|X-Y|$的表达式, 这里$X$和$Y$是相互独立的随机变量.     

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In this paper an efficient estimation methodology for the partially linear models with random effects is proposed. For this, we use the generalized least square estimate (GLSE) and the B-splines methods to estimate the unknowns, and employ the penalized least square method to obtain the estimators of the random effects item. Further, we also consider the estimation for the variance components. Compared with the existing methods, our proposed methodology performs well. The asymptotic properties of the estimators are obtained. A simulation study is carried out to assess the performance of our proposed methodology.     

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Let p_M(t,x,y) be the minimal heat kernel of a d-dimenional compact Riemannian manifold M for any time t\in(0,1] and x,y\in M. Using the horizontal Brown bridge on M, we prove that, for any nonnegative integers n and m, there is a constant C depending on n,m and the manifold M, such that |\nabla^n_x\nabla^m_y\ln p_M(t,x,y)|\leq C[d(x,y)/t+1/\sqrt{t}\,]^{n+m}$, which generalizes the conclusion of the higher derivatives of the logarithmic heat kernel \ln p_M(t,x,y) about single variable in \ncite{1}.     

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This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,i\geq1\} is a sequence of independent, identically distributed and real-valued random variables and the weights {\theta_i,i\geq1\} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the F belongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability.     

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In this paper, we introduce the definitions of geometric strongly ergodic, strongly ergodic and weakly ergodic for continuous-state Markov chains, then we give a primary proof of equivalence of the ergodicities for continuous-state Markov chains.     

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??The Bayesian model are established for the VaR and related risk measurements. The relationship between VaR and other risk measurements including expect shortfall, tail condition expectation and conditional value at risk are discussed. Furthermore, the Bayesian estimates and Bayesian predictors of these risk measurement are derived. Thirdly, the consistency and asymptotic normality in the exponential risk model are proved. Finally, the numerical simulation method is used to verify the convergence rate under different sample sizes.     

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The discriminatory processor sharing queues with multiple classes of customers (abbreviated as DPS queues) are an important but difficult research direction in queueing theory, and it has many important practical applications in the fields of, such as, computer networks, manufacturing systems, transportation networks, and so forth. Recently, researchers have carried out some key work for the DPS queues. They gave the generating function of the steady-state joint queue lengths, which leads to the first two moments of the steady-state joint queue lengths. However, using the generating function to provide explicit expressions for the steady-state joint queue lengths has been a difficult and challenging problem for many years. Based on this, this paper applies the maximum entropy principle in the information theory to providing an approximate expression with high precision, and this approximate expression can have the same first three moments as those of its exact expression. On the other hand, this paper gives efficiently numerical computation by means of this approximate expression, and analyzes how the key variables of this approximate expression depend on the original parameters of this queueing system in terms of some numerical experiments. Therefore, this approximate expression has important theoretical significance to promote practical applications of the DPS queues. At the same time, not only do the methodology and results given in this paper provide a new line in the study of DPS queues, but they also provide the theoretical basis and technical support for how to apply the information theory to the study of queueing systems, queueing networks and more generally, stochastic models.     

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In this article, using the limit theory of martingales, we study the moderate deviation for maximum likelihood estimator of unknown parameter in the stochastic partial differential equation driven by additive fractional Brownian motion with Hurst parameter, and the rate function can be calculated. Moreover, we apply our main result to several examples.     

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This paper studies the estimation of change point in mean and variance function of a non-parametric regression model based on kernel estimation and wavelet method. First, kernel estimation of mean function is developed and it is used to estimate the position and jump size of mean change. Second, wavelet methods are applied to derive the variance estimator which is used to estimate the location and jump size of the change point in variance. The asymptotic properties of these estimators are proved. Finally, the results from a numerical simulations and comparison study show that validate the effectiveness of our method.     

关于能量距离的两点注记（英文）

本文讨论了能量距离的两个问题.类似Brownian协方差的讨论提出了Brownian距离的定义,并证明了Brownian距离与能量距离的一致性.给出了配对变量的能量距离的表示,并探讨了将能量距离用于配对样本同分布的检验问题时原假设下的渐近分布理论.最后通过一个简单的数值模拟说明基于能量距离的配对样本的分布差异的检验方法比传统的t检验及Wilcoxon符号秩检验更有效.     

关于保持距离相等映射和逼近满等距算子的两个注记(英文)

在本文中,给出经典等距理论领域中的两个注记.关于FulviaSkof[1]的结果,用于赋范空间的严格凸性的研究,用Voft定理[2]给出这个著名结果的推广,并且我们的证明比原证明更短.此外,指出实Banach空间上的逼近满等距算子和有限维空间上的一般等距算子都是线性的,从而知道满射条件是本质的.     

Minimum Distance Estimation in AR(1)-processes

In this paper a new minimum distance estimator is defined in case that the residuals of an AR(1)-process are contaminated normally distributed. This estimator is asymtotically normally distributed and in most cases less biased than the least square estimator. Furthermore, a method is presented to numerically calculate the minimum distance estimator as a root of an implicit function.     

图的距离谱综述

设D(G)为连通图G的距离矩阵,λ1(D)≥>…≥AnD)是D(G)的特征值.距离特征值的研究可追溯到Graham 和Pollack [Bell Syst.Tech.J.,1971,50:2495-2519]的工作,其中描述了负距离特征值数目与数据通信系统寻址问题之间的关系.2014年,Aouchiche和Hansen...     

关于Simpson公式的两个注记

对Simpson公式的积分余项作出渐近估计,并给出了Simpson公式反问题的一个结果.     

关于拓扑熵下界的两点注记

设ｆ：Ｘ→Ｘ是紧连通多面体自映射，应用Ｎｉｅｌｓｅｎ不动点理论，我们给出了ｆ的拓扑熵ｈ（ｆ）的一个更好下界。另外，若ｆ：Ｔ^m→T^m是ｍ－环面自映射，我们还得到了ｌｏｇＮ^∞（ｆ）是{h(g)|g≈f:T^m→T^m}的下确界的一个充要条件，这里Ｎ（ｆ）是ｆ的渐近Ｎｉｅｌｓｅｎ数，从而局部解答了姜伯驹教授提出的一个问题。     

环境制约条件下含两菌株寄生虫的传染模型

研究了环境制约条件下含两菌株寄生虫的传染模型,结合流感病毒的传播规律,考虑同一亚型不同毒株之间的传染病模型.讨论了模型各个平衡点的存在条件,局部渐近稳定的条件,并对模型进行了数值模拟,很好的验证了模型的相关性质和特点.     

Sufficient Dimension Reduction via Distance Covariance

We introduce a novel approach to sufficient dimension-reduction problems using distance covariance. Our method requires very mild conditions on the predictors. It estimates the central subspace effectively even when many predictors are categorical or discrete. Our method keeps the model-free advantage without estimating link function. Under regularity conditions, root-n consistency and asymptotic normality are established for our estimator. We compare the performance of our method with some existing dimension-reduction methods by simulations and find that our method is very competitive and robust across a number of models. We also analyze the Auto MPG data to demonstrate the efficacy of our method. Supplemental materials for this article are available online.     

方差未知时两样本正态混合模型齐-性的修正似然比检验

本文讨论了方差未知时检验两样本正态混合模型齐一性的修正似然比统计量的极限性质,证明了原假设下修正似然比统计量的渐近分布为自由度为1的卡方分布.     

On Upper Bounds for Minimum Distance and Covering Radius of Non-binary Codes

We consider upper bounds on two fundamental parameters of a code; minimum distance and covering radius. New upper bounds on the covering radius of non-binary linear codes are derived by generalizing a method due to S. Litsyn and A. Tietäväinen lt:newu and combining it with a new upper bound on the asymptotic information rate of non-binary codes. The upper bound on the information rate is an application of a shortening method of a code and is an analogue of the Shannon-Gallager-Berlekamp straight line bound on error probability. These results improve on the best presently known asymptotic upper bounds on minimum distance and covering radius of non-binary codes in certain intervals.