New estimators of distribution functions

ABSTRACT

This article considers the estimation of a distribution function F_X(x) based on a random sample X₁, X₂, …, X_n when the sample is suspected to come from a close-by distribution F₀(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F₀(x). As a by-product similar estimators are proposed for population quantiles.     

Edge Estimation in the Population of a Binary Tree Using Node-Sampling

Suppose a finite population of several vertices, each connected to single or multiple edges. This constitutes a structure of graphical population of vertices and edges. As a special case, the graphical population like a binary tree having only two child vertices associated to parent vertex is taken into consideration. The entire binary tree is divided into two sub-graphs such as a group of left-nodes and a group of right-nodes. This paper takes into account a mixture of graph structured and population sampling theory together and presents a methodology for mean-edge-length estimation of left sub-graph using right edge sub-graph as an auxiliary source of information. A node-sampling procedure is developed for this purpose and a class of estimators is proposed containing several good estimators. Mathematical conditions for minimum bias and optimum mean squared error of the class are derived and theoretical results are numerically supported with a test of 99% confidence intervals. It is shown that suggested class has a sub-class of optimum estimators, and sample-based estimates are closer to the true value of the population parameter.     

亚里土多德和孔子的政体理论比较研究

孔子和亚里士多德分别是古代东西方最伟大的政治家、思想家 ,在东西方政治思想史上都占有极重要的地位。前人对他们政治思想的研究颇多 ,但对比研究则少 ,文章拟通过对他们政体理论的比较研究 ,找出东西方文化差异根源     

SOME REMARKS ON THE MEAN, MEDIAN, MODE AND SKEWNESS

Many sufficient conditions for inequalities about the mean, median, mode and skewness have been obtained. The paper presents a theorem that unifies already known results, gives some counter-examples, and considers the cases of Pearson distributions.     

圆光栅细分误差的动态测量

本文讨论了圆光栅细分误差及其测量,提出了不采用高精度标准件的圆光栅细分误差测量法——时间平均法,并通过实际测试结果证明了时间平均法的可行性。     

狂野爱情的毁灭——从电视剧《金锁记》谈改编艺术

电视剧<金锁记>在遵循原作内在精神的基础上,从不同的角度糅合了现代人的审美特质,与现代人产生共鸣.改编后的<金锁记>所带来的艺术效果是强烈的,为改编艺术提供了一种参考和借鉴.     

A Correction Note on Improvement in Variance Estimation Using Auxiliary Information

ABSTRACT

In this paper, the testing problem for homogeneity in the mixture exponential family is considered. The model is irregular in the sense that each interest parameter forms a part of the null hypothesis (sub-null hypothesis) and the null hypothesis is the union of the sub-null hypotheses. The generalized likelihood ratio test does not distinguish between the sub-null hypotheses. The Supplementary Score Test is proposed by combining two orthogonalized score tests obtained corresponding to the two sub-null hypotheses after proper reparameterization. The test is easy to design and performs better than the generalized likelihood ratio test and other alternative tests by numerical comparisons.     

现代金融学理论的缺陷与解决路径

标准金融学与行为金融学的根本分歧是市场是否具有有效性。作为标准金融学基石的有效市场假说的致命缺陷是检验时点有效,即在任何一个时点上证券价格都即时、准确地反映所有信息,这一理想化的约束条件不仅使该理论的应用价值大打折扣,也使其存在着巨大的理论缺陷。行为金融学正是抓住这一点对其提出了质疑和挑战。在推翻标准金融学的理论假设后的行为金融学也没有建立一个比标准金融学更有实际应用性的学说体系,其应用性甚至远远落后于被其否定的以CAPM、APT、OPT等为代表的标准金融学理论。市场有效周期理论认为,市场有效是一个时期而不是一个时点,通过实证研究可以对该理论进行检验。市场有效周期理论的重要价值主要是在解决标准金融学和行为金融学的分歧上实现了重大突破。     

《金锁记》改写的背后

《金锁记》是张爱玲作品中唯一一篇充满斗争激越、呼应“五四”主题的文章。改写后的《怨女》则成为超越时代局限 ,走向人性深处 ,带有普泛性和恒定性主题的文章。在张爱玲的文学趣味向传统复归的背后 ,是作者对“五四”文学的反思 ,以及对中国文艺的表现方式、表现题材的寻求。