基于Adaptive-Lasso的本科成绩统计分析

本文主要研究了合肥工业大学数学学院数学专业学生的本科成绩状况,应用多元线性统计方法,探讨了前期所有课程成绩对后期成绩的影响.首先对前期课程进行主成分分析,并采用逐步回归方法建立了后期成绩与主成分之间的回归模型.其次,采用Adaptive-Lasso方法建立后期成绩与前期课程成绩间的Adaptive-Lasso回归模型.最后,对以上模型进行对比分析.研究表明,基于Adaptive-Lasso方法的主成分回归模型能很好地拟合后期成绩,并对后期成绩情况给出合理的解释.     

大学生在校成绩与高考成绩的统计分析

通过对合肥工业大学机械与汽车工程学院07级毕业生的高考成绩与本科期间在校成绩进行统计分析,研究发现高考成绩与在校的学期成绩有较大的相关性,且高考成绩对在校学期成绩的影响因专业的不同而不同.同时对部分代表性课程与高考成绩、已学课程成绩进行了统计建模,并就大学学习的特点及影响大学成绩的各个因素进行了讨论.     

全面成绩管理的初探

利用数量化方法,数字特征法,W ilcoxon顺序和检验法以及试卷分析的各种方法(试题难度,区分度,信度,效度等),定量地解决了影响学生成绩的主要因素,并引入全面管理方法,明显地改善了学生成绩,学生综合能力明显加强.     

浅谈高三后期数学复习备考

离高考还剩下最后几十天了,我们还能做些什么呢?成绩是否还能有所提升?很多同学都很彷徨.其实,后期的每一分钟都很重要,都有可能提高自己的成绩,只要科学合理地安排,充分利用好每一分钟,都会卓有成效.     

怎樣帮助數學成績較差的學生逐步地提高到一般水平

我校(嘉定中学)行政上前曾明确地向我们数学教师提出:“对于成绩较差的同学;教师应予以重点帮助,使能逐步地提高到一般水平.”当时在我们的思想上认为这个工作是一个额外负担,觉得成绩较差的学生,主要是天资愚笨,平时不用功.因而就产生了抗拒思想,不愿意很好地进行帮助工作,但通过了前年暑期思想改造,我们初步树立了工人阶级的思想,也初步地认清人民教师的光荣感和责任感.在这基础上,各位     

2008年中国足球超级联赛成绩与技术统计的因子分析

通过查阅资料,收集、并整理了2008年中超联赛15支队伍210场比赛的技术统计.运用因子分析法对比赛成绩与技术统计的关系进行了研究,命名并分析影响比赛成绩的5个因子.旨在揭示统计指标与比赛成绩的特点与规律,为我国足球运动的理论与训练提供科学依据。     

基于主成分分析与最优分割理论对实习成绩综合评定的研究与分析

教育实习成绩评定是师范类学校很重要的内容,但评价过程受主观因素影响多及指标间相关性的影响.根据系统工程原理,采用SA S软件在构建评价指标体系和应用多元统计分析中主成分分析法和最优分割法的基础上,给出了一种综合评判教育实习成绩水平的新方法,结果表明它可为公平、公正的对学生成绩评定提供重要的参考作用.     

高等数学成绩影响因素分析——以沈阳师范大学为例

在本科一年级理工类学生中进行问卷调查,获取高等数学成绩影响因素的样本数据.利用因子分析测量问卷的结构效度,并实现对影响成绩各因素的正交化变换,为进一步的最优尺度回归提供筛选变量的依据.采用最优尺度回归分析来探索高等数学成绩的影响因素,结合教学实际,对各因素进行有针对性地分析,提出改进教学效果的建议和措施.     

基于增值的中学教学效率评估模型

分析了在中学教学质量评价中引入“增值”概念的意义与作用 ,讨论了协方差分析法与齐次马尔柯夫链分析法的理论依据及其计算程序 ,并结合四所中学的数据进行了实际分析 ,解决了因各校学生高中入学成绩存在差异而无法正确地以学生高考成绩评价中学教学质量问题 .     

沈燮昌的学术成就与贡献——沉痛悼念我师沈燮昌教授

公元一九九一年九月十九日下午六时十分,敬爱的沈燮昌先生——著名函数逼近专家、北京大学数学系和数学研究所教授,因患癌症医治无效不幸与世长辞了.从此数学界失去了一个精英,函数逼近论研究领域失去了一位名家,我们失去了一位良师益友.燮昌先生一九三四年九月十日生于浙江海宁县.从小就聪明伶俐,勤奋好学,于一九五二年以异的成绩考入北京大学数学力学系.在北大学习期间成绩总是名列前茅,大学毕业又以成异的成绩考入莫斯科数学研究所作研究生,一九六一年获苏联理学副博士学位.同年回国执教     

Double-Scan Statistics

Researchers frequently scan sequences for unusual clustering of events. Glaz et al. (2001) survey scan statistic tools developed for these analyses. Many of these tools deal with clustering of one type of event. In other applications the researcher scans for clusters of two types of events, A and B. Consider a sequence of D independent and identically distributed trials where each trial has one of four possible outcomes: A ^c B ^c , A B ^c , A ^c B, A B. When the events A and B occur within d consecutive trials, we say that a two-type d-cluster has occurred (a directional cluster is also defined that requires that the A event comes at least as early as the B event). Naus and Wartenberg (1997) develop a double scan statistic that counts the number of declumped (a type of non-overlapping) clusters that contain at least one of each of two different types of events. They derived the expectation and variance and Poisson approximation for the distribution of the double scan statistic. The approximation and declumping methods used work well when the events are relatively rare but not as well for the case where the two types of events occur with high frequency. This paper develops an alternative family of double scan statistics to count the number of non-overlapping two-type d-clusters. These new double scan statistics behave similarly to the Naus-Wartenberg statistic for rare events, but capture other information for the more dense event case. Exact and approximate results are derived for the distribution of the new double scan statistics, allowing its use for a wider range of density of events. The double scan statistics are compared for the epidemiologic application in Naus and Wartenberg, and for a molecular biology application involving genome versus genome protein hits.     

Statistics of orderings

In this paper, we study a Ramsey type problems dealing with the number of ordered subgraphs present in an arbitrary ordering of a larger graph. Our first result implies that for every vertex ordered graph G on k vertices and any stochastic vector \(\overrightarrow{a}\) with k! entries, there exists a graph H with the following property: for any linear order of the vertices of H, the number of induced ordered copies of G in H is asymptotically equal to a convex combination of the entries in \(\overrightarrow{a}\). This for a particular choice of \(\overrightarrow{a}\) yeilds an earlier result of Angel, Lyons, and Kechris. We also consider a similar question when the ordering of vertices is replaced by the ordering of pairs of vertices. This problem is more complex problem and we prove some partial results in this case.     

Combinatorial Statistics on Alternating Permutations

We consider two combinatorial statistics on permutations. One is the genus. The other, , is defined for alternating permutations, as the sum of the number of descents in the subwords formed by the peaks and the valleys. We investigate the distribution of on genus zero permutations and Baxter permutations. Our q-enumerative results relate the statistic to lattice path enumeration, the rank generating function and characteristic polynomial of noncrossing partition lattices, and polytopes obtained as face-figures of the associahedron.     

Second-order Linearity of Wilcoxon Statistics

The rank statistic , with R _i (t) being the rank of and e ₁ , . . . , e _n being the random sample from a distribution with a cdf F, is considered as a random process with t in the role of parameter. Under some assumptions on c _i , x _i and on the underlying distribution, it is proved that the process converges weakly to the Gaussian process. This generalizes the existing results where the one-dimensional case was considered. We believe our method of the proof can be easily modified for the signed-rank statistics of Wilcoxon type. Finally, we use our results to find the second order asymptotic distribution of the R-estimator based on the Wilcoxon scores and also to investigate the length of the confidence interval for a single parameter β _l .     

Wave Statistics in Non-Linear Random Sea

The sea elevation at a fixed point is modeled as a sum of a Gaussian process plus a quadratic random correction term. It is shown that the process can also be written as a quadratic form of a vector valued Gaussian process with arbitrary mean. The saddlepoint method is used to approximate the intensity (u), say, the sea level crosses the level u. The accuracy of the proposed method is studied. In examples the computed intensity is used to bound the wave crest distribution. The bounds are compared with empirical distributions derived from simulations.     

浅谈概率论与数理统计的教学

概率论与数理统计跟其它的数学分支课程相比,有其特殊的思维模式．本文主要从激发学生学习兴趣、平行概念类比教学、锻炼概率思维,N重视“辨误”数学四个方面阐述了如何搞好概率统计课的教学．     

"Freezing" and "defreezing" effects in the photoelastic investigation of temperature stresses

The "freezing" and "defreezing" temperature limits of an optically active material based on an epoxy resin have been experimentally investigated. A method of determining the mean value of the optical coefficient when the material is heated on the "freezing" temperature range is considered. The lower "defreezing" temperature limit has been experimentally established. The results of the investigation are presented in the form of graphs.Translated from Mekhanika Polimerov, No. 3, pp. 501–506, May–June, 1976.     

Estimating Averages of Order Statistics of Bivariate Functions

We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis. As an application, uniform estimates for the expected value of averages of order statistics of sequences of independent random variables in terms of Orlicz norms are obtained. In the case where the bivariate functions are matrices, we provide a “minimal” probability space which allows us to C-embed certain Orlicz spaces \(\ell _M^n\) into \(\ell _1^{cn^3}\), with \(c,C>0\) being absolute constants.     

Invariance Principles for Paced Record Times and Applications

Let {Y_n:n0} be a sequence of independent and identically distributed random variables with continuous distribution function, and let {N(t):t0} be a point process. In this paper, making use of strong invariance principles, we establish limit laws for the paced record process {X(t):t0} based on {Y_n:n0} and {N(t):t0}. We consider as applications of our main results, the case of the classical and paced record models. We conclude by extensions of our theorems to non-homogeneous record processes.