Estimation for the Distribution of Two-dimensional Discrete Scan Statistics

This paper concerns the application of the method introduced in (Haiman, Extremes, 3:349–361, 2000) to estimate the distribution of two-dimensional discrete scan statistics. This method makes it possible to establish sharp bounds for the estimation errors. The method involves the estimation by simulation of the distribution of scan statistics for the particular rectangle sets of size 2×2, 2×3, 3×3, where the unit is the (m ₁×m ₂) dimension of the rectangular scanning window, m ₁, m ₂ ∈ℕ. We perform several numerical applications and compare our results with results obtained by other authors.      

Estimating the Distributions of Scan Statistics with High Precision

In many statistical applications one is concerned with the estimation of the distribution of the maximum or minimum number of points in a moving window of fixed length, called scan statistics. Scan statistics are also extremes of 1-dependent sequences. A result of Haiman (1999) provides approximations of these distributions together with sharp bounds for the corresponding errors. Applications concern the maximum cluster of points on a line or on a circle and multiple coverage by subintervals or subarcs of fixed size. We compare our method with some existing empirical and non empirical methods and show how it can be applied to multidimensional scanning     

扫描统计量--检测基金业绩持续性的新方法

基金业绩持续性检测的一般方法是横截面回归与列联表分析，都是从基金行业层面整体检测持续性，不能有效的检测单只基金的业绩持续性。为此本文引入一种新的检测方法——扫描统计量，可以创新性地对单只基金进行有效分析。利用扫描统计量方法对我国基金业绩持续性进行了实证分析，发现部分基金存在持续性，给出了持续性强度的上限，为投资者买卖基金、基金业绩考核、风险监控提供了决策参考依据。     

从扫描统计量角度观察我国连续暖冬现象

从1986年以来我国连续出现全国性暖冬,引起了国内外学者的广泛关注."暖冬"不仅直接影响到生态环境和生态平衡等以及人类的生产与日常活动,还会对政治、经济产生重大的影响,也越来越受到人们的普遍关注。本文引入扫描统计量,对暖冬连续出现的概率进行计算,以分析其异常程度。分析结果表明,无论按照过去对暖冬划分的旧标准还是2002年起使用的新标准,我国连续出现的暖冬现象都属于显著异常的,需要引起气候环境工作者和公众的重视和警觉。     

A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process

A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a perfect simulation algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.     

Evaluation of Spatial Scan Statistics for Irregularly Shaped Clusters

Spatial scan statistics are commonly used for geographic disease cluster detection and evaluation. We propose and implement a modified version of the simulated annealing spatial scan statistic that incorporates the concept of “non-compactness” in order to penalize clusters that are very irregular in shape. We evaluate its power for the simulated annealing scan and compare it with the circular and elliptic spatial scan statistics. We observe that, with the non-compactness penalty, the simulated annealing method is competitive with the circular and elliptic scan statistic, and both have good power performance. The elliptic scan statistic is computationally faster and is well suited for mildly irregular clusters, but the simulated annealing method deals better with highly irregular cluster shapes. The new method is applied to breast cancer mortality data from northeastern United States.     

概率论与数理统计课程改革的创新机制

针对课程改革的目的,结合教学实践,就概率统计课程建设和教学改革的必要性进行综合分析并主张：通过讲述概率统计理论发展史,引导学生明确学习重点;借助多媒体教学,整合教学大纲内容,系统教学;将理论与实际相联系,激发学生学习兴趣;立足基本理论,开设统计学软件实验课程．     

Semi-parametric Estimation of the Second Order Parameter in Statistics of Extremes

We present a class of semi-parametric estimators for the second order parameter related to a probability distribution with a regularly varying tail. The second order parameter plays an important role whenever dealing with optimization problems in statistics of extreme values. Consistency and asymptotic normality are proven under appropriate conditions.     

若干笛卡尔积图的邻点可区别E-全染色

图G(V,E)的k是一个正整数,f是V(G)∪E(G)到{1,2,…,k}的一个映射,如果u,v∈V(G),则f(u)≠f(v),f(u)≠f(uv),f(v)≠f(uv),C(u)≠C(v),称f是图G的邻点可区别E-全染色,称最小的数k为图G的邻点可区别E-全色数.得到了Pm×Pn,Pm×Cn,Cm×Cn的邻点可区别E-全色数,其中C(u)={f(u)}∪{f(uv)uv∈E(G)}.     

漫谈统计学的应用与发展(3)

本文分两部分:第一部分通过20多个实际案例说明统计学在各个领域的广泛应用,希望使更多的人对统计学有更全面、更深切的了解;第二部分简要介绍统计学在国内外的发展概况,并通过其发展进程的介绍,进一步阐明统计学的意义与价值。同时列举更多的论据说明近代统计学是当今最重要的科学技术之一。     

漫谈统计学的应用与发展(1)

本文分两部分:第一部分通过20多个实际案例说明统计学在各个领域的广泛应用,希望使更多的人对统计学有更全面、更深切的了解;第二部分简要介绍统计学在国内外的发展概况,并通过其发展进程的介绍,进一步阐明统计学的意义与价值。同时列举更多的论据说明近代统计学是当今最重要的科学技术之一。     

漫谈统计学的应用与发展(2)

本文分两部分:第一部分通过20多个实际案例说明统计学在各个领域的广泛应用,希望使更多的人对统计学有更全面、更深切的了解;第二部分简要介绍统计学在国内外的发展概况,并通过其发展进程的介绍,进一步阐明统计学的意义与价值。同时列举更多的论据说明近代统计学是当今最重要的科学技术之一。     

漫谈统计学的应用与发展(4)

本文分两部分:第一部分通过20多个实际案例说明统计学在各个领域的广泛应用,希望使更多的人对统计学有更全面、更深切的了解;第二部分简要介绍统计学在国内外的发展概况,并通过其发展进程的介绍,进一步阐明统计学的意义与价值。同时列举更多的论据说明近代统计学是当今最重要的科学技术之一。     

Asymptotic Bound on the Characteristic Function of Signed Linear Serial Rank Statistics

This work establishes an asymptotic bound on the characteristic function of signed linear serial rank statistics. The result is obtained under rather general conditions including the important case of van der Waerden scores. It generalizes the result of Seoh (1983, Ph.D. Thesis, Department of Mathematics, Indiana University) and constitutes an essential step to the elaboration of Berry-Esséen's bounds and the establishment of Edgeworth expansions. These statistics constitute a natural tool for testing the hypothesis of white noise with a symmetrical (unspecified) distribution in comparison to other alternative hypothesis of serial dependence.     

Queue tests for renewal processes

Queuing models can be used to test whether a stochastic point process can be represented as a renewal process. The test queuing model is analyzed, perhaps by simulation, using the prrocess of interest to generate arrivals or service times. Various congestion measures indicate departure from the renewal property.     

注重统计思想的现代工科概率统计教学方法

指出了工科概率统计教学中长期存在而又被忽视的一个问题,即学生的统计计算能力有余而对于统计思想、统计方法的理解与使用不足.并尝试着提出了注重统计思想的现代统计教学方法.     

二面体群的小度数Cayley图的同构类的计数

设G是有限群,S是G的一个不包含单位元的非空子集且满足S^-1=S,定义群G关于S一个的Cayley图x=Cay(G,S)如下：V(X)=G,E(X)=｛(g,sg)｜g∈G,s∈S}.对于素数P,本文给出了2p阶的二面体群的3度和4度Cayley图的同构类的个数.     

稳健残差控制图的构建及在金融时序中的应用

对于呈现自相关和波动族聚性并存的受控过程,通常采用残差控制图对其进行监控。但异常点的存在会对自相关或波动族聚性模型的拟合产生重要影响,使得基于该模型的残差并非独立同分布导致常规残差控制图监控失效。为解决这类问题,本文提出稳健残差控制图。即建立稳健的ARMA模型解决自相关问题从而得到无自相关的残差序列,用稳健的GARCH模型来构建控制图的上下限。模拟和实证研究表明,本文提出的稳健残差控制图具有很好的抗异常点能力并能更好的对金融时间序列的异常现象进行监控。     

An Optimal Algorithm to Solve the All-Pairs Shortest Paths Problem on Permutation Graphs

In this paper we present an optimal algorithm to solve the all-pairs shortest path problem on permutation graphs with n vertices and m edges which runs in O(n ²) time. Using this algorithm, the average distance of a permutation graph can also be computed in O(n ²) time.     

基于加权相似性的BIRCH聚类算法

BIRCH方法是一个集成的层次聚类方法.它克服了凝聚层次聚类方法所面临的两个难点:可伸缩性和不能撤销前一步工作的问题.基于BIRCH聚类的多阶段聚类算法思想,结合基于权重的欧式距离度量和基于划分的K-means算法,提出了一种基于加权相似性的BIRCH聚类方法,并将方法应用在时间序列的气象数据分析中.