线性模型中参数向量的线性经验Bayes估计

本文利用线性经验Ｂａｙｅｓ估计的思想，对线性回归模型中未知参数向量构造了一类线性经验Ｂａｙｅｓ估计，并在一定条件下证明了其具有的ａ．ｏ．收敛速度．     

Bayes局部影响分析

本文从Ｂａｙｅｓ观点出发，利用Ｋｕｌｌｂａｃｋ－Ｌｅｉｂｌｅｒ距离和微分几何方法，系统地讨论了微小扰对于Ｂａｙｅｓ统计推断的局部影响，给出了Ｂａｙｅｓ局部影响分析的一般公式，作为应用，具体讨论了线性回归模型的Ｂａｙｅｓ估计和Ｂａｙｅｓ预测的局部影响问题，数值计算的结果表明，本文的方法是比较有效的。     

方差分析模型中参数的经验Bayes估计及其优良性问题

本文考虑单向分类的方差分析模型，构造了Ｐ′α的线性Ｂａｙｅｓ估计和经验Ｂａｙｅｓ（ＥＢ）估计，此处αａ×１是效应参数向量，Ｐａ×ｋ是常数矩阵．在较一般的条件下，基于均方误差矩阵准则和ＰｉｔｍａｎＣｌｏｓｅｎｅｓｓ准则，我们分别证明了ＥＢ估计优于最小二乘估计     

多维参数线性经验Bayes估计一致收敛速度的最优性

证明出任何一个多维参数性经验Ｂａｙｅｓ估计的一致收敛速度不可能超过１，从而说明文［１］中构造的线性经验Ｂａｙｅｓ估计的一致收敛速度１是最优的。     

二项分布可靠度的Bayes,多层Bayes估计

本文给出了二项分布可靠度的Ｂａｙｅｓ估计、多层Ｂａｙｅｓ估计，并对一些结果进行了比较。     

截尾试验下指数分布的贝叶斯估计

在指数分布场合，定数或定时截尾试验，文［１］给出了参数λ在先验分布为Γ（α，β）分布的假设下的Ｂａｙｅｓ估计．文［３］给出了在平方损失下的Ｂａｙｅｓ估计．本文讨论先验分布为Ｂ（ａ，ｂ）分布时，参数λ的Ｂａｙｅｓ估计．     

模糊Bayes检验

本文对原假设和备择假设中参数是模糊子集的假设检验问题，引入了模糊Ｂａｙｅｓ检验的概念，对简单模糊假设，给出了求模糊Ｂａｙｅｓ检验的方法，讨论了它的性质，并针对一类特殊的隶属函数，得出了检验的具体公式。最后，通过几个数值实例，表明了模糊Ｂａｙｅｓ检验的优良性。     

次序统计量给出的线性Bayes估计

本文讨论了位置尺度参数族的参数线性函数的线性Ｂａｙｅｓ估计问题，给出了基于次序统计是的线性Ｂａｙｅｓ估计，并就特殊分布给出了例子。     

线性模型回归系数EB估计的一致收敛速度

利用多元密度函数及其导数的核估计方法，建立了多元线性模型回归系数的经验Ｂａｙｅｓ估计，并给出了这种估计的一致收敛速度。     

Г─Г结构串联系统可靠度的Bayes估计

本文把含于结构系统中应力和强度含有的未知参数视为随机变量，利用Ｂａｙｅｓ方法讨论了当应力和强度均服从Г分布时结构串联系统可靠度θ＝Ｐ（Ｘ＞Ｙ）的估计问题，给出了θ的Ｂａｙｅｓ置信限。     

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.     

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.     

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.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.