Stochastic orderings related to ranking in an nth order record process

Let X₁, X₂, …, X_m be successive observations on m objects, numbered 1,2, …, m. If X₁ belongs to the n largest observations among X₁,X₂,…,X_i, object i is called a record, i = 1,2,…,m; n?1.In investigating the influence of the ranking of the objects on the expected number of records, a hierarchy of stochastic order relations between random variables arises.It is these order relations and their relationship with known stochastic orderings that are studied in this paper.     

压铸机合模机构的正交回归优化设计

在对压铸机合模机构的优化设计中,采用正交回归设计法建立结构性能与设计变量的近似函数,对近似函数进行优化,从而有效地解决了结构优化设计过程中优化方法需要反复进行三维有限元分析而引起的超大计算量问题;这种方法对实际应用中大量存在而又无法得到解析式的结构优化问题有着普遍的意义。     

运用“3P”教学法提高少数民族中学生英语素质

“3P”即“Presentati on Acti vities Practice Activities”和“Production Activities”, 运用“3P”教学法改变了传统的“注入式”教学法, 对提高少数民族中学生的英语素质具有十分重要的意义。     

Z-4-(对-溴苯硫基)-3-(对-硝基苯甲酰氧基)-3-丁烯-2-酮的立体选择性合成和Diels-Alder反应活性研究

合成了一个新的α ,β取代 3-丁烯 - 2 -酮 (CH3COC(p -NO2 C6 H4 COO - ) =CH-S -C6 H4 Br - p) (4) ,用元素分析 ,核磁共振波谱和X -衍射对其结构进行了表征 ,并对其构型和Diels -Alder反应活性进行了探讨 .结果表明只有Z构型的产物生成 ,Z - 4 -溴 - 3-(对一硝基苯甲酰氧基 ) - 3-丁烯 - 2 -酮可与丁二烯型化合物发生Diels -Alder反应 ,而标题化合物在相似条件下不能发生Diels -Alder反应     

S—完全正则与S—完全正规空间

文章引入了S－完全正则（S3．5）空间与S－完全正规（S5）空间的概念,讨论它们各自的特征性质以及与其他Si－空间的相互关系。     

Sharp upper bounds for the expected values of non-extreme order statistics from discrete distributions

We consider the problem of determining sharp upper bounds on the expected values of non-extreme order statistics based on i.i.d. random variables taking on N values at most. We show that the bound problem is equivalent to the problem of establishing the best approximation of the projection of the density function of the respective order statistic based on the standard uniform i.i.d. sample onto the family of non-decreasing functions by arbitrary N  -valued functions in the norm of L²(0,1)$L^2(0,1)$ space. We also present an algorithm converging to the local minima of the approximation problems.     

局部空间自相关指标对比研究

本文研究了最常用的局部空间自相关指标;局部Moran指数和局部G系数,基于模拟的空间区域;设计了一些有代表性的空间聚集方案进行计算,比较了两种指标的探测结果,得出局部G系数要优于局部Moran指数的初步结论。     

Efficiency of weighted averages

When combining estimates of a common parameter (of dimension d?1$d?1$) from independent data sets—as in stratified analyses and meta analyses—a weighted average, with weights ‘proportional’ to inverse variance matrices, is shown to have a minimal variance matrix (a standard fact when d=1$d=1$)—minimal in the sense that all convex combinations of the coordinates of the combined estimate have minimal variances. Minimum variance for the estimation of a single coordinate of the parameter can therefore be achieved by joint estimation of all coordinates using matrix weights. Moreover, if each estimate is asymptotically efficient within its own data set, then this optimally weighted average, with consistently estimated weights, is shown to be asymptotically efficient in the combined data set and avoids the need to merge the data sets and estimate the parameter in question afresh. This is so whatever additional non-common nuisance parameters may be in the models for the various data sets. A special case of this appeared in Fisher [1925. Theory of statistical estimation. Proc. Cambridge Philos. Soc. 22, 700–725.]: Optimal weights are ‘proportional’ to information matrices, and he argued that sample information should be used as weights rather than expected information, to maintain second-order efficiency of maximum likelihood. A number of special cases have appeared in the literature; we review several of them and give additional special cases, including stratified regression analysis—proportional-hazards, logistic or linear—, combination of independent ROC curves, and meta analysis. A test for homogeneity of the parameter across the data sets is also given.     

Convex rearrangements,generalized Lorenz curves,and correlated Gaussian data

We propose a statistical index for measuring the fluctuations of a stochastic process ξ$\xi$. This index is based on the generalized Lorenz curves and (modified) Gini indices of econometric theory.