再谈足球与不等式

文[1]中提出一个有趣的问题：足球与不等式,现摘录如下：某学校进行足球冠军赛,比赛采用单循环制,即每个球队都和其余球队进行一场比赛．先规定好每场比赛中,胜队得2分,败队得0分,出现平局两队各得1分．比赛结果是有一队的得分最高,超过其他任何球队的分数,但它所赢得的场数却比其他任何球队都少．少     

稳健的惩罚经验似然方法及压缩估计

本文基于原有的经验似然函数,在经验似然的约束条件中的估计方程上加入Huber函数和权重函数,将经验似然方法和稳健估计方程相结合,再在目标函数中加上SCAD惩罚函数,提出一种稳健的变量选择和惩罚估计方法.通过数值模拟与最小二乘估计和普通的惩罚经验似然估计在变量选择和参数估计方面进行比较,显示本文所提出的基于惩罚稳健经验似然的压缩估计具有明显优势.     

近似空间与信任结构之间的关系

回顾了由二元关系产生的粗糙近似空间及其导出的各种粗糙近似算子的构造性定义,介绍了经典和模糊环境下各种信任结构及其导出的信任函数与似然函数的概念,给出了粗糙集理论中近似空间及其导出的下近似算子与上近似算子和证据理论中的信任结构及其导出信任函数与似然函数之间的相互关系及其应用背景。     

用Excel软件实现最大似然估计数值计算的方法

本文给出用Excel软件实现最大似然估计数值计算求解的方法。内容包括对似然方程求数值解、直接对似然函数或对数似然函数求极大值以及分组数据最大似然估计的数值计算。     

多重Ⅲ型删失数据场合Logistic分布参数的近似似然函数

在多重型删失数据场合,利用ML法做统计推断时,由于似然函数过于复杂,常遇到很大困难.通过文中方法我们获得了Logistic分布参数的近似似然函数,并在大样本场合,证明此似然函数以概率1收敛于原似然函数.     

多重Ⅱ型删失数据的近似似然函数及应用

多重Ⅱ型删失数据是一种很常见的数据删失类型，处理起来也非常困难，本文获得了多重Ⅱ型删失数据的一种近似似然函数，并证明了在大样本场合下，这种近似与似然函数是等价的。基于该近似似然函数，求得了参数的近似极大似然估计与近似Bayes估计，并讨论似极大似然估计的性质。     

多重Ⅱ型删失数据场合 Logistic 分布参数的近似似然函数

在多重Ⅱ型删失数据场合,利用ML法做统计推断时,由于似然函数过于复杂,常遇到很大困难.通过文中方法我们获得了 Logistic 分布参数的近似似然函数,并在大样本场合,证明此似然函数以概率1收敛于原似然函数.     

非线性模型中的拟似然估计和约束拟似然估计

该文证明了,在非线性回归模型中,若以均方误差或均方误差矩阵为标准,拟似然估计是正则广义拟似然估计类中的最优估计,并讨论了拟得分函数最优性与拟似然估计最优性的关系.为改进拟似然估计,该文提出了一种约束拟似然估计,并证明了约束拟似然估计比拟似然估计有较小的均方误差.     

基于截断Poisson分布的Marshall—Olkin拓展分布

采用复合分布的方法,将一个参数λ和一个已有分布组合成一个新的分布的方法,研究新分布与原分布之间的DFR的继承性和似然序关系.在原分布分别取为指数分布和正态分布时,分析其密度函数和危险率函数的等统计特征.最后,用一组数据进行实证研究,利用极大似然估计估计出参数,分别用指数扩展分布和指数分布拟合进行比较.     

非线性回归模型中的约束拟似然

在非线性回归模型中,拟得分函数是一类线性无偏估计函数中的最优者(GodambeandHeyde(1987),朱仲义(1996)),而由拟得分函数得到的拟似然估计在由线性无偏估计函数得到的估计类中具有渐近最优性(林路(1999)).本文则研究非线性回归模型中的有偏估计函数理论,构造了参数的约束拟似然估计,得到了约束拟似然的局部最优性,局部改进了拟似然估计,从而扩充了线性模型中的有偏估计理论.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.