基于投影寻踪和最优分割的企业信用评级模型

提出一种基于投影寻踪和最优分割的企业信用评级模型。该模型运用投影寻踪对样本企业进行信用综合评分,将信用综合得分由大到小排序,生成有序样品序列;利用最优分割法对有序样品进行聚类,得出明确的聚类结果;将最优分割点对应的信用综合得分作为划分信用等级的阈值,从而实现对样本企业的信用评级。应用实例证明了该模型的可行性和有效性。     

基于加权马尔可夫链预测方法最优分组的实证分析研究

在介绍加权马尔可夫链预测方法的基础上,以昆明市东川区1956年至2000年的年降雨量为实例,分别基于样本均值-均方差分组法和有序聚类分组法(最优分割法)进行加权马尔可夫链滚动预测的实证分析.结果表明有序聚类分组法比均值-均方差分组法更为合理.     

一种基于谱聚类分析的粒子群聚类算法

本文研究了谱聚类中NJW算法的样本最优划分问题.利用粒子群算法在聚类问题上搜索到的全局最优,获得了NJW算法对聚类样本的最优划分.推广了谱聚类算法在样本划分时的普适性和稳定性.实验对比验证该算法是有效的.     

多指标综合评价方法及其优化选择研究

本文分三部份：１）用等级次序检验解决多种综合评价方法的优化选择；２）根据综合评价值，用有序聚类方法对样本划分级别；３）实证分析。     

二维有序样本的有约束系统聚类

二维有序样本进行聚类必须满足两个要求：（１）类内各单元的相似性和类间的差异性；（２）各单元在位置上的有序性和类内的连通性。根据这些要求，将各单元观测指标间的距离矩阵作为聚类的指示矩将各单元之间的区位联系矩阵作为聚类的约束矩阵，在约束矩阵给出的约束条件之下，以类间单元指标的最大距离作为类间相似性指标，在指示矩阵中通过逐步聚并而将全部单元合并归类，即可得出满足要求的样本分类。     

模糊C均值算法的改进

模糊聚类分析方法具有较强的实用性,但传统的模糊C均值算法对数据集进行分类时有均分的趋势,对于数据集中各类样本数目相差较大的情况,其聚类结果不是很理想.因此,本文对FCM算法进行了改进,使之不但能够达到更好的分类效果,同时也更加适用于样本分类不均衡的聚类问题.文中还结合具体算例进行了聚类分析,得到了理想的分类效果.     

最优分割法的适用性及一类有序样品的聚类方法

确定.当 n,k 固定时,e[p(n,k)]越小,则各类直径越小,分类越合理.由此,最优分割方法的基点在于选定离差平方和作直径,并使各类总的离差平方和达到最小进行分类.采用这种标准,对于有确定趋势的有序样品,[1]给出了不适用的例子.由于离差平方和为各样品离开均值(?)_(ij)的分散程度的度量,因此,上述最优分割法只就同类样品离散程度小,类间离散程度大进行分类,即构成一类的样品离均值具有大致相同的分散程度.然     

一类新的最优分割法及其应用

本文对最优分割法的目标进行了改造,提出了一类新的最优分割法,包括六种最优分割法 M1—M6.通过实例计算,发现新方法的分类性能指标有了明显改进.最后,把离散多目标规划方法与最优分割法结合起来,提出了一种寻求最优分类的协调型最优分割法.     

非对称Possion跳——扩散模型的参数估计

受有序样本聚类思想的启发,本文针对期权定价模型中的非对称Possion跳———扩散模型,提出了一种基于标的资产价格历史数据的参数估计方法,并得到了较好的结果。     

平面有序样品的PP聚类

本文给出平面有序样品的ＰＰ聚类方法，并对ＰＰ指标及Ｐ聚类的性质进行了理论讨论。     

Analysis of Curve Reconstruction by Meshless Parameterization

This paper proposes and analyzes a method called meshless parameterization for reconstructing curves from unordered point samples. The method solves a linear system of equations based on convex combinations so as to map the sampled points into corresponding parameter values, whose natural ordering provides the ordering of the points. Using the theory of M-matrices, we derive natural conditions on the point sample which guarantee the correct ordering. A sufficient condition is that the underlying curve be tangent-continuous and free of self-intersections and that the sample is dense enough.     

商业银行财务绩效偏序集评价研究

为了提高商业银行财务绩效水平,满足利益相关者信息需求,从收益和风险以及发展的角度构建“盈利性”、“安全性”、“流动性”和“社会性”四个维度的商业银行财务绩效评价指标体系,采用偏序集评价方法对15家样本商业银行2017年财务绩效进行评价。财务绩效排名和HASSE图的结果表明:处于较高层级的样本商业银行财务绩效较好,其盈利性、安全性、流动性较优,并具备较强的发展能力;处于较低层级的样本商业银行财务绩效较差,其盈利性、安全性、流动性较弱,发展能力较弱;重要性程度靠前的 “盈利性”和“安全性”评价维度,不是导致商业银行绩效排名和分层的主要影响因素,商业银行要提升财务绩效,应该更加重视“流动性”和“社会性”维度。同时,采用偏序集评价方法,克服了评价指标精确赋权问题,获得的HASSE图直观展示样本商业银行财务绩效排名稳定性和整体市场竞争格局,具备其他评价方法无法比拟的优势。     

可靠性系列知识讲座 第一讲:可靠性的基本统计知识

介绍了可靠性的基本概念、数据类型、寿命分布、参数估计,特别是用于计算置信限和置信区间的统计量方法和样本空间排序法。     

Estimating Stochastically Ordered Survival Functions via Geometric Programming

Many procedures have been proposed to compute nonparametric maximum likelihood estimators (NPMLEs) of survival functions under stochastic ordering constraints. However, each of them is only applicable to a specific type of stochastic ordering constraint and censoring, and is often hard to implement. In this article, we describe a general and flexible method based on geometric programming for computing the NPMLEs from right- or interval-censored data. To this end, we show that the monotonicity properties of the likelihood function and the stochastic ordering constraints considered in the literature allow us to reformulate the estimation problem as a geometric program (GP), a special type of mathematical optimization problem, which can be transformed to a convex optimization problem, and then solved globally and efficiently. We apply this GP-based method to real data examples to illustrate its generality in handling different types of ordering constraints and censoring. We also conduct simulation studies to examine its numerical performance for various sample sizes. Supplemental materials including technical details, computer code, and data files are available online.     

求参数置信限的一种方法

本文介绍一种找参数精确置信限和置信区间的一般方法,关键想法是在样本空间中定义一个序。本文主要考虑单参数统计模型，对序的优良性（即相应的置信限的优良性）作了讨论，指出应以得分函数的大小为依据在样本空间中定义序。还证明了用最大似然估计定义序得到的置信限是一个单调函数的唯一零点，从而通过解方程算出置信限。     

工业企业经济和环境综合效益的集对分析

应用集对分析中的同异反态势排序法进行了重点工业污染源资源消耗和排污状况分析.实例分析表明,该方法和评价模型具有简单实用的特点.     

Truncated Sequential Test for a Proportion and it's Sample Space Ordering Method

This paper proposes a new sampling plan, the sample space ordering method, to compute the optimum truncated sequential test in order to overcome the disadvantages of the widely use sequential sampling methods that IEC1123 has presented. The main ideal of this new method is to establish an order at the truncated sequential sample space, and optimize point by point to arrive the optimal truncated sequential test. The paper presents in detail how to realize the new plan, and shows that this new plan has most powerful to control the sample number and least average sample number comparing with the methods which IEC1123 and SMT have proposed.     

The level probabilities for a simple loop ordering

Bartholomew's statistics for testing homogeneity of normal means with ordered alternatives have null distributions which are mixtures of chisquared or beta distributions depending on whether the variances are known or not. The mixing coefficients depend on the sample sizes and the order restriction. If a researcher knows which mean is smallest and which is largest, but does not know how the other means are ordered, then a loop ordering is appropriate. Exact expressions for the mixing coefficients for a loop ordering and arbitrary sample sizes are given for five or fewer populations and approximations are developed for more than five populations. Also, the mixing coefficients for a loop ordering with equal sample sizes are computed. These mixing coefficients also arise in testing the ordering as the null hypothesis, in testing order restrictions in exponential families and in testing order restrictions nonparametrically.This research was supported by the National Institutes of Health under Grant 1 R01 GM42584-01A1     

Expected cost bounds for the selection and ordering procedures based on binary-type questions

The problems considered in this paper are similar to those studied by Arrow, Pesotchinsky and Sobel (1981). We search for the optimal methods of ordering of a sample or of identifying sample order statistics by asking binary type questions and employing the criterion which defines the cost of a question as the number of responses. The asymptotic results show that our procedures with simple algorithms are comparable (in terms of cost) with the best known methods for ordering by using pairwise comparisons.     

排序法计算指数寿命型元件串联系统可靠性经典精确最优置信下限

对于样本点是离散的情况,可用对样本点排序的方法确定可靠性置信下限,排序有很多种,有L-P排序、序贯排序、极大似然估计排序、修正L-P排序等。本文提出一种具有直观合理性的新的排序方法,计算指数寿命型元件串联系统可靠性经典精确最优置信下限。