区间数据情形下线性模型的经验似然推断

§1Introduction Instatisticalapplications,weoftenencounterintervalcensoreddatawhenafailure timeYcannotbeobserved,butcanonlybedeterminedtolieinanintervalobtainedfroma sequenceofexaminationtimes.Forinstance,themaximumdosagewhichpatientscan endureisconcerned.LetYibethemaximumdosagewhichtheithpatientcanendure,Ui,j(j=1,2,...,k)bethedosagewhichthepatienthasbeentested.ItisobviousthatYiis unobservable.SupposetheithpatientisnormalwhenthedosageisUi,j,andhe(orshe)is abnormalwhenthedosageisUi,j+1.Then…     

On tail behavior of nonlinear autoregressive functional conditional heteroscedastic model with heavy-tailed innovations

We study the tail probability of the stationary distribution of nonparametric non- linear autoregressive functional conditional heteroscedastic (NARFCH) model with heavy- tailed innovations.Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance.When the innovations are heavy-tailed,the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations.We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the con- ditional variance function.Some examples are given.     

物流服务供应商联盟构建及分析

在分析供应链环境下物流服务运作的基础上,建立了信息对称情况下物流服务供应商分散控制和集中控制策略模型,并从物流服务联盟的总体产出效果和物流服务联盟对盟员利润的影响两个方面对其进行了定量分析,结果表明,建立物流服务联盟有利于增加联盟产出,抑制竞争对手的产出;如果物流服务企业之间有增加合作利润的需要,则都有建立联盟的积极性.最后对物流服务联盟的实现机理进行了分析.     

序约束下AR(p)-ARCH(q)模型参数的估计与检验

In this paper, we study a stationary AR(p)-ARCH(q) model with parameter vectors a and β. We propose a method for computing the maximum likelihood estimator (MLE) of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order: α1≥α2≥…≥αq, andβ1≥β2≥…βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio (LR) test statistic for the testing problem and derive its asymptotic null distribution.     

一类递归关系模型的求解方法

递归关系不仅在数学中有广泛应用,而且在计算机算法设计与分析中也有广泛应用.本文对Josephus问题进行了推广,得到一类更广泛的递归关系模型.讨论了这类模型的求解方法,采用d-进制记数法,给出了这类递归关系模型的解.     

存在不精确数据情况下的环境效率分析

针对环境效率评价问题中存在不精确数据的一类典型问题进行了深入的分析,在回顾现有的不精确数据处理方法以及环境效率评价方法的基础上,基于加性DEA模型,提出一种新的环境效率评价方法.该方法不仅能够求解各个投入/产出数据的最佳精确值,而且能够进一步分析各个决策单元的无效性.通过算例分析对模型及方法的优越性进行了说明,提出的方法克服了现有不精确数据处理方法的局限性,能够有效地处理环境效率分析问题中的不精确数据,得到更为准确的环境管理信息,为环境管理提供更为有效的决策依据.     

团队中枢节点的效率模型

集团性是社会网络的显著特征.团队作为一个小规模的社会网络,也存在网络结构的非均匀性以及中枢节点.在阐述团队网络的集团性和中枢节点导致网络的两面性等结构特征的基础上,运用小世界模型的局部效率和集聚系数等指标,建立了团队中枢节点的效率模型,并通过网络结构的调整(如加键和断键重连)研究了网络结构对中枢节点的效率的影响.     

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work (Levine and Peres, Indiana Univ Math J 57(1):431–450, 2008). For the shape consisting of sites, where ω _d is the volume of the unit ball in , we show that the inradius of the set of occupied sites is at least r − O(logr), while the outradius is at most r + O(r ^α ) for any α > 1 − 1/d. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with n = πr ² particles, we show that the inradius is at least , and the outradius is at most . This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions, improving on bounds of Fey and Redig. Yuval Peres is partially supported by NSF grant DMS-0605166.     

On V-orthogonal projectors associated with a semi-norm

For any n ×  p matrix X and n ×  n nonnegative definite matrix V, the matrix X(X′V X)⁺ X′V is called a V-orthogonal projector with respect to the semi-norm , where (·)⁺ denotes the Moore-Penrose inverse of a matrix. Various new properties of the V-orthogonal projector were derived under the condition that rank(V X) =  rank(X), including its rank, complement, equivalent expressions, conditions for additive decomposability, equivalence conditions between two (V-)orthogonal projectors, etc.     

New global stability conditions for a class of difference equations

In this paper we consider some classes of difference equations, including the well-known Clark model, and study the stability of their solutions. In order to do that we introduce a property, namely semicontractivity, and study relations between ‘semi-contractive’ functions and sufficient conditions for the solution of the difference equation to be globally asymptotically stable. Moreover, we establish new sufficient conditions for the solution to be globally asymptotically stable, and we improve the ‘3/2 criteria’ type stability conditions.