散度偏大计数数据分布的贝叶斯估计

本文针对索赔次数数据的特点, 讨论了两类可导致散度偏大特征数据的分布类型: 零点膨胀分布与膨胀参数分布, 并根据Bayes理论与MCMC方法, 利用WinBUGS对其进行建模和抽样\bd 经过比较,给出了实现分布拟合的途径, 最后通过两个数值例子加以展示.     

Panel Count Data模型参数的经验似然推断

对Panel Count Data的处理越来越受到人们的关注,Sun与Wei^([1-2])基于简单的半参数模型,提出了Panel Count Data的回归分析,并且给出了参数的估计方程。本文则基于经验似然的思想,讨论了上述Panel Count Data模型参数的置信域构造问题,特别仅通过经验似然置信区域给出了参数估计的方差阵估计,证明了估计的1/n相合性。基于Sun与Wei所给的数据,给出了参数置信区域的具体构造过程和结果。通过作图比较可以看出经验似然置信域要优于依据渐近正态性所构造的置信域。我们还依据所作出的经验似然置信域对参数估计的方差矩阵进行了估计,与用传统渐近正态性得到的矩阵较为接近。     

零膨胀集群数据层次回归模型的贝叶斯推断

零膨胀Poisson回归模型是研究零观测值过多的计数数据的常用工具,本文提出了一类拟合具有这类特征的集群数据的层次零膨胀泊松回归模型,并给出了相应的贝叶斯推断方法,参数估计通过Gibbs抽样获得,模型比较与选择则通过拟合优度检验与BIC准则实现.最后,利用一个船舶受损事故数据来展示本文方法的实现及应用.     

利用计数统计模型方法评价大连星海公园旅游的经济价值

在非市场条件下如何评价旅游资源的经济价值是自然旅游公园管理工作中所面临的一个重要问题.正确地估计这类公园的旅游需求函数则是对其有效地进行经济价值评价的关键.由于旅游次数数据具有非负整数和截断的性质,使用传统的多元线性回归模型来估计旅游需求函数则会产生较大的偏差.因此。本文采用非线性最小二乘、截断泊松分布和截断负二项分布等计量经济学模型估计大连星海公园的旅游需求函数,以此来计算公园旅游的经济价值。     

Cross-ranking of Decision Making Units in Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a mathematical model that evaluates the relative efficiency of Decision Making Units (DMUs) with multiple input and output. In some applications of DEA, ranking of the DMUs are important. For this purpose, a number of approaches have been introduced. Among them is the cross-efficiency method. The method utilizes the result of the cross-efficiency matrix and averages the cross-efficiency scores of each DMU. Ranking is then performed based on the average efficiency scores. In this paper, we proposed a new way of handling the information from the cross-efficiency matrix. Based on the notion that the ranking order is more important than individual efficiency score, the cross-efficiency matrix is converted to a cross-ranking matrix. A cross-ranking matrix is basically a cross-efficiency matrix with the efficiency score of each element being replaced with the ranking order of that efficiency score with respect to the other efficiency scores in a column. By so doing, each DMU assume the role of a decision maker and how they voted or ranked the other DMUs are reflected in their respective column of the cross-ranking matrix. These votes are then aggregated using a preference aggregation method to determine the overall ranking of the DMUs. Comparison with an existing cross-efficiency method indicates a relatively better result through usage of the proposed method.     

一个积和式计数公式的等价形式及其证明

给出了一个积和式计数公式在图论意义下的一般表达式 ,并证明了它们之间的等价关系     

A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis

The efficiency measures provided by DEA can be used for ranking Decision Making Units (DMUs), however, this ranking procedure does not yield relative rankings for those units with 100% efficiency. Andersen and Petersen have proposed a modified efficiency measure for efficient units which can be used for ranking, but this ranking breaks down in some cases, and can be unstable when one of the DMUs has a relatively small value for some of its inputs. This paper proposes an alternative efficiency measure, based on a different optimization problem that removes the difficulties.     

Properties of Some Character Tables Related to the Symmetric Groups

We determine invariants like the Smith normal form and the determinant for certain integral matrices which arise from the character tables of the symmetric groups S_n and their double covers. In particular, we give a simple computation, based on the theory of Hall-Littlewood symmetric functions, of the determinant of the regular character table _RC of S_n with respect to an integer r 2. This result had earlier been proved by Olsson in a longer and more indirect manner. As a consequence, we obtain a new proof of the Mathas Conjecture on the determinant of the Cartan matrix of the Iwahori-Hecke algebra. When r is prime we determine the Smith normal form of _RC. Taking r large yields the Smith normal form of the full character table of S_n. Analogous results are then given for spin characters.Partially supported by The Danish National Research Council.Partially supported by NSF grant #DMS-9988459.     

列联表信息相关系数的统计检验

针对度量列联表行列变量相关强度的信息相关系数,本文利用信息相关系数的概率函数,提出了信息相关系数P值法的理论检验方法,由于该方法计算量大,在实际应用中需要用简单的方法来取代。对简单的四格表,通过理论分析和计算机模拟,验证了P值法可用确切概率法取代,而确切概率法又可用简单的X~2法来取代。在此基础上,将X~2检验法推广到一般列联表的信息相关系数的检验,从而较好地解决了列联表相关系数从检验到计算的问题。     

On the Reconstruction of a String from Spectral Data

We consider the problem to reconstruct the mass distribution of a string where the mass is concentrated in a finite number of points, or, equivalently, the problem to reconstruct a simply connected mass spring system with unknown masses and stiffness parameters if the following data are given. Problem 1: The spectra of the string and of a modification of the string, or. Problem 2: The spectra of two different modifications of the string. Here a modification of the string is a string which appears if we link the unknown string with another string of known mass distribution. The paper contains a necessary condition for the existence of a solution of Problem 1, and explicit formulas and an algorithm for the solutions of the Problems 1 and 2 under the condition that there exists a solution. For the case that the mass distribution of the unknown string is not discrete we consider the problem to find discrete approximations of this distribution from the respective spectral data. The methods are based on the spectral theory of generalized second order differential operators as developed by M. G. Krein     

基于决策者风险偏好大数据分析的大群体应急决策方法

针对重大突发事件应急决策大群体成员的风险偏好复杂难测问题,提出了一种新的基于决策者风险偏好大数据分析的大群体应急决策方法。首先专家群体对突发事件进行快速响应,生成若干应急预案及其风险属性信息;其次,社会公众通过网络等渠道参与到应急决策中来并形成决策大群体,给出不同预案的偏好值;然后,利用证据推理算法得出公众对各预案的风险效用值,将预案风险效用值与预案偏好值加权组合,得到各个预案的大群体决策者的风险偏好值;最后,基于风险偏好值,利用大数据分析技术对大群体的风险偏好进行聚类识别,从中筛选出风险中立者组成新的应急决策群体,再次聚类得出应急决策群体的成员组成结构,以此为基础计算决策者权重和应急预案的最终效用值,得应急预案排序结果。最后通过算例分析验证了方法的有效性和可行性。     

Character Tables of Parabolic Subgroups of the Chevalley Groups of Type G 2

The main aim of this paper is to construct the character tables of the parabolic subgroups of the Chevalley groups G ₂(q), where q is a power of a prime p > 3.     

A Comparison of Data Envelopment Analysis and Artificial Neural Networks as Tools for Assessing the Efficiency of Decision Making Units

This paper is concerned with the comparison of two popular non-parametric methodologies—data envelopment analysis and artificial neural networks—as tools for assessing performance. Data envelopment analysis has been established since 1978 as a superior alternative to traditional parametric methodologies, such as regression analysis, for assessing performance. Neural networks have recently been proposed as a method for assessing performance. In this paper, we use a simulated production technology of two inputs and one output for testing the success of the two methods for assessing efficiency. The two methods are also compared on their practical use as performance measurement tools on a set of bank branches, having multiple input and output criteria. The results demonstrate that, despite their differences, both methods offer a useful range of information regarding the assessment of performance.