Approximating moments of continuous functions of random variables using Bernstein polynomials

Bernstein polynomials have many interesting properties. In statistics, they were mainly used to estimate density functions and regression relationships. The main objective of this paper is to promote further use of Bernstein polynomials in statistics. This includes (1) providing a high-level approximation of the moments of a continuous function $g\left(X\right)$ of a random variable $X$, and (2) proving Jensen’s inequality concerning a convex function without requiring second differentiability of the function. The approximation in (1) is demonstrated to be quite superior to the delta method, which is used to approximate the variance of $g\left(X\right)$ with the added assumption of differentiability of the function. Two numerical examples are given to illustrate the application of the proposed methodology in (1).     

一致性分数阶优化灰色模型及其应用

传统的分数阶灰色预测模型在时间序列预测中具有较好的适应性和预测的有效性,但其累加和差分计算式比较复杂。一致性分数阶累加相对于一般的分数阶累加,形式更简单,更便于计算和理论推导。为了提高模型的适应性和预测能力,文章在CFGM(1,1)白化方程中引入一个新的可变系数,扩大了原有白化方程的适用范围,并在此基础上构建了一致性分数阶优化灰色模型,即CFOGM(1,1)模型。最优一致性分数阶阶数和可变系数通过PSO算法最小化平均相对误差获得。将构建的模型运用到两个实例中并与其他经典的灰色预测模型进行对比,结果表明所提出的模型具有较高的拟合和预测精度。     

WTO与汽车工业发展战略:整车还是零部件优先

在分析、对比我国零部件工业和整车产业经济绩效的基础上 ,文章认为零部件工业尽管先天不足 ,但却取得了更好的经济绩效 ,同时 ,由于相对比较低的进入壁垒以及加入 WTO之后面向全球化的竞争 ,零部件工业的竞争力和发展前景应该比整车产业要好一些。在此基础上 ,提出加入 WTO之后 ,应该优先发展零部件工业 ,在零部件已有一定基础的前提下 ,放开政策 ,扩大轿车作为消费品的需求 ,从而拉动整个汽车工业的发展     

Getting Unstuck: Interdisciplinarity as a New Discipline

Most disciplines and subdisciplines consider their particular specialization to be valuable in itself and superior to other disciplines. But compared with the huge leaps in the physical sciences, the social/behavioral sciences and humanities have made little progress. Since many of the physical science advances were the result of the merging of disciplines, perhaps interdisciplinarity should be tried. One path to connecting disciplines, subdisciplines, and micro‐macro levels is suggested by Spinoza's idea of part/whole methodology, exactly balancing concrete instances with abstract theses. Ideas by B. Pascal, A. Koestler, A. N. Whitehead, and E. O. Wilson may also be helpful. Any discipline, subdiscipline, or level can serve as a valuable stepping‐off place, but to advance further, integration with at least one other viewpoint may be necessary. Two brilliant examples are The Civilizing Process, by the sociologist Norbert Elias, and Freudian Repression, by the psychologist Michael Billig. Koestler's idea of “bi‐sociation” may prove to be particularly rewarding. The way that Virginia Woolf's depiction of role‐taking in interior monologue preceded the idea in social science is an extraordinary example. The need for integration may be the single most important issue facing social science, the humanities, and their subdisciplines. Given the scope of the social/behavioral problems faced by humanity, the sooner the better.     

New Goodness-of-Fit Tests Based on Sample Quantiles

In this article power divergences statistics based on sample quantiles are transformed in order to introduce new goodness-of-fit tests. Quantiles of the distribution of proposed statistics are calculated under uniformity, normality, and exponentiality. Several power comparisons are performed to show that the new tests are generally more powerful than the original ones.     

Cutting Experimental Designs into Blocks

Most experimental material in agriculture and industry is heterogeneous in nature and therefore its statistical analysis benefits from blocking. Many experiments are restricted in time or space, and again blocking is useful. This paper adopts the idea of orthogonal blocking of Box & Hunter (1957) and applies it to optimal blocking designs. This approach is then compared with the determinant-based approach described in the literature for constructing block designs.     

On the power of durbin-watson statistic against fractionally integrated processes

This paper provides the theoretical explanation and Monte Carlo experiments of using a modified version of Durbin-Watson ( D W ) statistic to test an 1 ( 1 ) process against I ( d ) alternatives, that is, integrated process of order d, where d is a fractional number. We provide the exact order of magnitude of the modified D W test when the data generating process is an I ( d ) process with d E (0. 1.5). Moreover, the consistency of the modified DW statistic as a unit root test against I ( d ) alternatives with d E ( 0 , l ) U ( 1 , 1.5) is proved in this paper. In addition to the theoretical analysis, Monte Carlo experiments show that the performance of the modified D W statistic reveals that it can be used as a unit root test against I ( d ) alternatives.     

略论毛泽东与人民民主

毛泽东毕生为争取人民民主而奋斗,从为人民争取民主到为人民享受民主而殚精竭虑。他主张要扩大民主,吸引广大人民群众直接参加国家管理,确保人民民主权利的实现,以此根治官僚主义和坚持社会主义方向。     

静电旋风除尘器性能的研究

在分析离心和静电分离综合作用的基础上，建立了修正的平衡轨道模型．利用该半经验模型．可较好地说明静电分离和离心分离作用两者对静电旋风除尘器除尘性能的影响．利用所建立的除尘实验装置，系统地进行了静电旋风除尘器性能实验研究，着重分析了除尘器进口风速、工作电压、电晕极型式和布置方式等因素对除尘器性能的影响．     

“网运分离”模式下我国铁路运输业路运的竞争

为铁路运输业引入竞争以提高其效率,是一切改革方案的最终目的。“网运分离”模式为此提供了可能。虽然从理论上分析,“网运分离”后铁路运输业存在多种竞争形式,但真正有效的是线路运营权的竞争和与其它运输方式间的竞争两种。从有效竞争理论和可竞争市场理论分析,在我国铁路运输业引入竞争,需要政府、企业、社会多方面的努力。