Intradimensional Single-Peakedness and the Multidimensional Arrow Problem

Arrow's account (1951/1963) of the problem of social choice is based upon the assumption that the preferences of each individual in the relevant group are expressible by a single ordering. This paper lifts that assumption and develops a multidimensional generalization of Arrow's framework. I show that, like Arrow's original framework, the multidimensional generalization is affected by an impossibility theorem, highlighting not only the threat of dictatorship of a single individual, but also the threat of dominance of a single dimension. In particular, even if preferences are single-peaked across individuals within each dimension – a situation called intradimensional single-peakedness – any aggregation procedure satisfying Arrow-type conditions will make one dimension dominant. I introduce lexicographic hierarchies of dimensions as a class of possible aggregation procedures under intradimensional single-peakedness. The interpretation of the results is discussed.     

Power of Enforcement and Dictatorship

A new Arrovian impossibility is obtained without invoking independence of irrelevant alternatives type assumptions. The new conditions leading to the impossibility are based on the concept of power of enforcement, and specify how this power can (see A3) or cannot be expanded (see A1, A2 and A4).     

霍夫曼理论适合中国的工业化模式吗?——兼议新型工业化道路中的重化工业发展路径

霍夫曼理论是通过总结多国制造业部门不同历史阶段的数据,分析各国工业化过程中消费品和资本品工业部门的相对地位的变化而提出来的。该理论认为一国的工业化是资本品工业部门比重不断增大的过程。但是,由于历史阶段和分析技术的局限,霍夫曼理论只是对欧美发达国家工业化过程在事实层面上的描述和总结,并没有形成关于工业化一般路径的科学分析。因此,它还不具备普遍的指导意义。坚持以科学发展观和新型工业化道路的基本理念为指导,依靠技术创新和制度创新,以产业结构调整为主线,以合理规范的政府宏观调控作保证,是现阶段我国发展重化工业的基本路径。     

LOWER BOUNDS FOR THE NORMAL APPROXIMATION OF A SUM OF INDEPENDENT RANDOM VARIABLES

The rates of convergence to the normal distribution are investigated for a sum of independent random variables. Using Stein's method, we derive a lower bound of the uniform distance between two distributions of independent sum and normal.     

论间接测量数据处理的两种方法

评述了间接测量中标准偏差的两种方法，并探讨了造成它们两者之间差异的根源．     

可分Banach空间中的微分包含

在可分的Ｂａｎａｃｈ空间中研究微分包含ｘ′∈Ｆ（ｔ，ｘ）解的存在性，对Ｋｉｓｉｅｌｅｗｉｃｚ的结果作了改进．     

Asymptotics for multisample statistics

Consider a family of square-integrable R^d-valued statistics S_k = S_k(X_1,k1; X_2,k2;…; X_m,km), where the independent samples X_i,kj respectively have k_i i.i.d. components valued in some separable metric space X_i. We prove a strong law of large numbers, a central limit theorem and a law of the iterated logarithm for the sequence {S_k}, including both the situations where the sample sizes tend to infinity while m is fixed and those where the sample sizes remain small while m tends to infinity. We also obtain two almost sure convergence results in both these contexts, under the additional assumption that S_k is symmetric in the coordinates of each sample X_i,kj. Some extensions to row-exchangeable and conditionally independent observations are provided. Applications to an estimator of the dimension of a data set and to the Henze-Schilling test statistic for equality of two densities are also presented.     

层次分析法中逆序问题与其决策环境研究

研究了层次分析法中的逆序问题与其决策环境的关系，并对产生逆序现象的机理作了数学上的分析和定性的解释。文中还给出了多准则下排序的强保序定理。     

On the discretization of nonparametric isotropic covariogram estimators

In this article, we describe the discretization of nonparametric covariogram estimators for isotropic stationary stochastic processes. The use of nonparametric estimators is important to avoid the difficulties in selecting a parametric model. The key property the isotropic covariogram must satisfy is to be positive definite and thus have the form characterized by Yaglom's representation of Bochner's theorem. We present an optimal discretization of the latter in the sense that the resulting nonparametric covariogram estimators are guaranteed to be smooth and positive definite in the continuum. This provides an answer to an issue raised by Hall, Fisher and Hoffmann (1994). Furthermore, from a practical viewpoint, our result is important because a nonlinear constrained algorithm can sometimes be avoided and the solution can be found by least squares. Some numerical results are presented for illustration.