多元$t$分布数据的局部影响分析

对于多元$t$分布数据, 直接应用其概率密度进行影响分析是困难的\bd 本文通过引入服从Gamma分布的权重, 将其表示为特定多元正态分布的混合\bd 在此基础上, 进而将权重视为缺失数据, 引入EM算法; 从而利用基于完全数据似然函数的条件期望进行局部影响分析\bd 本文进一步系统研究了加权扰动模型下的局部影响分析, 得到了相应的诊断统计量; 并通过两个实例说明了这种方法的有效性.     

区间数据任意阶原点矩的估计

在生存分析和可靠性研究中, 区间数据的存在常常使得传统的统计方法无法直接使用\bd 本文从无偏转换的思想出发, 对区间数据的任意阶原点矩进行了估计\bd 当截断变量的分布密度函数已知时, 得到了一批具有强相合性(收敛速度可以达到$n^{-1/2}(\log\log n)^{1/2}$)和渐近正态性的估计量, 并通过模拟计算对这种估计方法的可行性和有效性进行了验证.     

重复试验随机效应模型误差方差的齐性检验$(k=2)$

本文对重复试验次数为2的随机效应方差分析模型, 给出了误差方差齐性, 即$H_0:\sigma_1^2 =\sigma_2^2\leftrightarrow H_1:\sigma_1^2\ne\sigma_2^2$的一种具有相合性的检验方法\bd 并对三个常见模型给出了检验统计量和拒绝域的具体表达式, 最后是两个应用实例\bd     

价值风险的非参数估计方法*

价值风险(VaR)模型是当今最流行的金融资产风险管理和控制的工具之一\bd 本文提出了用局部分位数回归的方法来估计某一投资组合的VaR值\bd 该方法可用于计算投资组合多持续期的VaR, 使得人们可以了解到该投资组合在一定持续期内的动态风险\bd 本文通过模拟和美国三个月到期国债利率数据的分析说明了该方法的具体执行情况, 并与J.P. Morgan的时间开方规则作了比较\bd 结果表明我们的VaR估计有令人满意的效果.     

混合指数分布的参数估计

混合指数分布是寿命数据分析中一个非常重要的统计模型\bd 但是利用正规的统计方法如矩估计、极大似然估计等估计模型的参数往往比较困难\bd 本文应用EM算法详细研究了混合指数分布在正常工作条件下和在进行恒加应力加速寿命实验条件下, 在完全数据场合、I-型截尾和II-型截尾场合的参数估计问题\bd 模拟说明利用EM算法来估计混合指数分布是一种非常有效的方法.     

广义线性度量误差模型

在线性度量误差模型中, 需要假设所有变量的观测值都含有未知度量误差\bd 因而 该模型不适用于一部分变量的观测值含有度量误差、而另一部分变量的观测值可精 确得到的情况\bd 为此, 本文提出了广义函数、结构和超结构关系线性度量误差模 型\bd 进一步, 这里还讨论了这些广义线性度量误差模型中参数的最小二乘和极大 似然估计方法, 给出了参数估计的表达式     

变量的有限混合模型对有序数据的Bayes聚类分析

本文基于隐变量的有限混合模型, 提出了一种用于有序数据的Bayes聚类方法\bd 我们采用EM算法获得模型参数的估计, 用BIC准则确定类数, 用类似于Bayes判别的方法对各观测分类\bd 模拟研究结果表明, 本文提出的方法有较好的聚类效果, 对于中等规模的数据集, 计算量是可以接受的.     

Erlang(2)过程的风险分析与美式看跌期权

在经典的风险理论中涉及到的索赔风险是服从复合Poission过程的, 与之不同, 我们考虑Erlang(2)风险过程\bd Erlang(2)分布往往见诸于控制理论中, 这里它作为索赔发生间隔时间的分布被引入了\bd 本文中, 我们介绍一个与破产时刻、破产前时刻的盈余以及破产时刻赤字有关的辅助函数$\phi(\cdot)$, 函数中涉及的这三个变量对风险模型的研究都是最基本也是最重要的\bdWillmot and Lin (1999)曾在古典连续时间风险模型之中研讨过这一函数\bd受Gerber and Shi(1997)及Willmot and Lin (2000)在古典模型下的研究过程的启发, 本文的一个重要结果就是找到破产前时刻的盈余以及破产时刻赤字的联合分布密度函数\bd 更得益于Gerber and Landry (1998)及Gerber and Shiu (1999)的思想, 我们应用以上的结果去寻求基础资产服从一定风险资产价格过程的美式看跌期权最优交易策略.     

用蒙特卡罗方法求取广义线性混合模型之最大似然估计:应用于求取乳癌死亡率之小区域估计

本文使用蒙特卡罗方法, 求得广义线性混合模型之最大似然估计, 并提供用来评估统计参数之收敛和精确度之实用方法\bd 仿真研究显示无偏之固定效应参数估计, 而方差分量估计之误差则相近于前人结果\bd 应用举例为使用泊松分布求取乳癌死亡率之小区域估计.     

时滞不确定性Markov切换线性随机微分系统的指数鲁棒稳定性

研究了一类时滞不确定性Markov切换随机微分系统的均方指数鲁棒随机稳定性\bd 系统中的时滞是时变的, 不确定项结构为范数有界, Markov切换是连续时间、离散状态的时齐Markov过程{\bf\!.} 利用随机Lyapunov函数方法和LMI技术, 得到了几个判定系统均方指数鲁棒随机稳定性的充分性条件\bd 一个数值例子说明了判据的有效性和可行性.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

基于平行DEA模型的我国小学教育资源配置效率分析

小学教育是教育阶段的基础,也是我国强制教育的一部分。但如何在各省份性别比例相差较大的情况下,更加有效的提高各省份小学教育资源配置效率是一个值得思考的问题。为了避免性别带来的影响,可以通过平行结构DEA模型根据学生性别分为两个平行子系统,来衡量我国2012~2018年各省份小学教育的资源配置情况。研究发现大部分省份小学教育资源配置的总系统效率未达到有效边界,仍有需要改进的地方。男学生在小学教育阶段的效率通常优于女学生在小学教育阶段的效率,但随着近些年我国教育体制的日益完善,女学生在小学教育阶段的效率呈上升趋势。此外,我国西部地区的小学教育资源配置效率在一些年份普遍优于东部和中部地区,而中部地区和东部地区小学教育总系统效率相对稳定,西部地区小学教育总系统效率波动较大。     

Sur la détermination d'une relation binaire à partir d'informations locales

This paper deals with the problematic aspect of the reconstruction of binary relations: it includes all the questions raising the possibility or impossibility to determine a structure by gathering given substructures. It is the continuation of three studies: the first made by G. Lopez [9] in 1972 about the determination of a binary relation through the types of isomorphism of its restrictions, the second made by K. B. Reid and C. Thomassen [15] in 1976 about the strongly self-complementary tournaments (every subtournament is self-complementary), the third made by C. Thomassen [16] in 1989 about the cycle space of a tournament. In the second section, we use the notion of class of difference (which was introduced in [9]) to extend a study made in [16] to binary relations. Then, in the third section, we improve the result of this last study in the case of the tournaments. After noticing that the result of [15] inferred itself naturally from the approach developed in [9], we extend, in the fourth section, the study made in [15] to binary relations.     

Rawlsian altruism with perfect discrimination leads to social efficiency

Recent studies draw attention on the highly specialized capacity of human beings in recognizing altruists versus cheaters in social interactions. These results hint at the existence of specialized abilities that support discriminating behavior in strategic interactions. In this paper, we explore the implications of discriminating behavior in the study of the indirect evolutionary selection of selfish versus altruistic motivations in the context of generic 2×2 base games, and in particular for coordination and cooperation scenarios. We find that inequality averse (Rawlsian) altruism can enforce under rather general conditions socially optimal outcomes, including cases where selfishness cannot, such as in prisoner’s dilemmas. Inequality seeking (Nietzschian) altruism in no case improves upon Rawlsian altruism in terms of social optimality of outcomes, and often does worse. In the cooperation scenario in particular, Nietzschean altruism never manages to implement the cooperative outcome. Under perfect discrimination, moreover, inequality averse (Rawlsian) altruism often evolves at the expense of selfishness. These results suggest that the development of sophisticated discrimination abilities may be strongly adaptive in supporting fairness-oriented forms of pro-sociality in humans in the context of social dilemmas and coordination problems.     

Mathematical modelling of social obesity epidemic in the region of Valencia,Spain

In this article, we analyse the incidence of excess weight in 24- to 65-year-old residents in the region of Valencia, Spain, and predict its behaviour in the coming years. In addition, we present some possible strategies to prevent the spread of the obesity epidemic.

We use classical logistic regression analysis to find out that a sedentary lifestyle and unhealthy nutritional habits are the most important causes of obesity in the 24- to 65-year-old population in Valencia. We propose a new mathematical model of epidemiological type to predict the incidence of excess weight in this population in the coming years. Based on the mathematical model sensitivity analysis, some possible general strategies to reverse the increasing trend of obesity are suggested.

The obese population in the region of Valencia is increasing (11.6% in 2000 and 13.48% in 2005) and the future is worrisome. Our model predicts that 15.52% of the population in Valencia will be obese by 2011. Model sensitivity analysis suggests that obesity prevention strategies (healthy advertising campaigns) are more effective than obesity treatment strategies (physical activity) involving the obese and overweight subpopulation in controlling the increase of adulthood obesity in the region of Valencia.     

火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.     

PANEL DISCUSSIONS

Representations of mathematical concepts play an important role in understanding: both in helping learners understand the to-be-learned material and in facilitating teachers’ understanding of pedagogical processes which, in turn, are involved in developing learners’ understanding. In this paper, we report on work with a cohort of pre-service primary teachers, with the aim of developing their understanding of mathematics, their confidence in their subject knowledge and their confidence in teaching mathematics. This was attempted through the introduction and use of a ‘representational approach’ to the teaching of the mathematical concepts required of teachers training to teach in primary schools in the UK. We present the results of attitude measures and a follow-up qualitative questionnaire in identifying whether and how the use of this representational approach supported pre-service teachers’ understanding and their confidence in teaching mathematics. The results suggest that the representational approach used had a positively significant impact on the attitudes towards studying and teaching mathematics.     

Exponential dispersion relation and its effects on unstable propagating pulses in unidirectionally coupled symmetric bistable elements

The propagation of pulses in unidirectionally coupled symmetric bistable elements is studied. The speeds of unstable traveling pulse waves in a ring of elements increase with pulse width in an exponential manner. This dispersion relation causes exponential increases in the duration of transient propagating pulses and the noise-sustained propagation of pulses, which are qualitatively the same as those in a reaction-diffusion-convection equation and a ring of sigmoidal neurons. However, the speeds of pulse fronts in propagating pulses depend on the backward pulse width. Properties of pulse transmission in an open chain of elements then differ from those in the above two systems qualitatively.     

Academics’ perceptions of the use and relevance of software in quantitative and financial disciplines

Software may be used in university teaching both to enhance student learning of discipline-content knowledge and skills, and to equip students with capabilities that will be useful in their future careers. Although research has indicated that software may be used as an effective way of engaging students and enhancing learning in certain scenarios, relatively little is known about academic practices with regard to the use of software more generally or about the extent to which this software is subsequently used by graduates in the workplace. This article reports on the results of a survey of academics in quantitative and financial disciplines, which is part of a broader study also encompassing recent graduates and employers. Results indicate that a variety of software packages are in widespread use in university programmes in quantitative and financial disciplines. Most surveyed academics believe that the use of software enhances learning and enables students to solve otherwise intractable problems. A majority also rate spreadsheet skills in particular as very important for the employability of graduates. A better understanding of the use of software in university teaching points the way to how curricula can be revised to enhance learning and prepare graduates for professional work.     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.