一类单参数假设检验拒绝域的直观构造法

本提出直观法的理论,举出用直观法构造单参数假设检验拒绝域的应用实例,并得出构造形如（*）式的检验拒绝的一种方法。     

变系数部分线性模型的拟合优度检验

本文考虑变系数部分线性模型的拟合优度检验问题.基于Profile经验似然方法,构造了参数部分和非参数部分的经验似然比检验统计量.并证明了其满足Wilks'现象,进而得到了一定置信水平的拒绝域.最后通过数据模拟,讨论了其检验功效.     

纵向部分线性模型的分块经验似然比检验

结合基函数逼近技术和分块经验似然方法,对纵向数据下的部分线性模型提出了一个简单有效的检验方法.在一定条件下,证明了所构造的检验统计量渐近服从标准卡方分布,进而得到了一定置信水平的拒绝域.数据模拟表明该检验方法可以有效地消除纵向数据的组内相关性对检验功效的影响.     

间隔涂色法

把图形按着一定的规律间隔地涂上颜色、把有色方格(点)和无色方格(点)看成被研究的对象,使研讨的问题变为直观,这种别具一格的解题方法称作间隔涂色法。某些数学竞赛试题,运用此法能起到意想不到的作用,对问题的理解、叙述、讨论都是有益的。下面从两方面谈谈此法的运用。一、用间隔涂色法构造命题“型模”某些数字命题的数量关系,能在间隔涂色法构造的“模型”上得到体现,直观地得到一种解释,从而得到问题的解答。例1 试用图解法证明 1+3+5+…+(2n-1)=n~2。解:用间隔涂色法构造图1,则命题的数量关系直观地体现出来。     

以功效函数为主线的假设检验教学

本文基于假设检验相关概念的统一,以及初等统计和高等统计学衔接的考虑,提出了以功效函数为主线的教学设计.首先基于证据原理确定拒绝域的形式,计算相应的功效函数;然后用功效函数描述假设检验的两类错误概率;最后根据给定的显著性水平运用功效函数确定拒绝域的具体形式.     

VaR的统计检验

根据VaR的基本原理,对VaR的有效性进行了讨论.关于VaR提出了一个基于二点分布的检验模型,证明了存在一致最优检验,并给出了检验的表达式和拒绝域,同时鉴于金融数据的庞大性,又提出了基于渐近正态分布的检验模型,给出了检验的表达式和拒绝域.     

第二类分数Ornstein-Uhlenbeck过程中参数估计的偏差不等式与Cramér-型中偏差

本文利用多重Wiener-Ito积分的偏差不等式和中偏差结果,得到第二类分数Ornstein-Uhlenbeck(OU)过程漂移项系数最小二乘估计量的若干渐近性质,其中包括偏差不等式和Cramér-型的中偏差;同时,给出以上估计量自正则版本的渐近性质,并以此构造漂移项系数的置信区间估计和显著性检验中的拒绝域(第二类错误以指数速度趋于0).     

给一不等式新的证法

不等式>1)的常规证法是“分子有理化”,即令,然后证明 今用“构造法”证明之,则更为直观: 构造 Rt△ABC和Rt△ABD(如图),使 则 在 一目了然.     

可用状态矩阵法分析的语言及状态矩阵的构造

状态矩阵法是语言编译的基本方法之一(见[1],[2])。本文阐明了可用状态矩阵法进行语法分析的语言特征,提出了系统地设置状态、构造状态矩阵的直观方法——树谱法。     

关于伽马函数与贝塔函数关系的证明

从gamma函数的函数定义法出发,利用MATLAB绘制出gamma函数延拓图像,给出出gamma函数的直观理解,采用构造法以及Laplace变换和卷积变换来证明gamma函数和beta函数关系,从而拓展学生的证明思路,为教师教学提供参考．     

Multi-frame representations in linear inverse problems with mixed multi-constraints

This paper is concerned with linear inverse problems where the solution is assumed to have a sparse expansion with respect to several bases or frames. We were mainly motivated by the following two different approaches: (1) Jaillet and Torrésani [F. Jaillet, B. Torrésani, Time–frequency jigsaw puzzle: Adaptive multi-window and multi-layered Gabor expansions, preprint, 2005] and Molla and Torrésani [S. Molla, B. Torrésani, A hybrid audio scheme using hidden Markov models of waveforms, Appl. Comput. Harmon. Anal. (2005), in press] have suggested to represent audio signals by means of at least a wavelet for transient and a local cosine dictionary for tonal components. The suggested technology produces sparse representations of audio signals that are very efficient in audio coding. (2) Also quite recently, Daubechies et al. [I. Daubechies, M. Defrise, C. DeMol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. 57 (2004) 1413–1541] have developed an iterative method for linear inverse problems that promote a sparse representation for the solution to be reconstructed. Here in this paper, we bring both ideas together and construct schemes for linear inverse problems where the solution might then have a sparse representation (we also allow smoothness constraints) with respect to several bases or frames. By a few numerical examples in the field of audio and image processing we show that the resulting method works quite nicely.     

Transformations in the Visual Representation of a Figural Pattern

Multiple representations of a given mathematical object/concept are one of the biggest difficulties encountered by students. The aim of this study is to investigate the impact of the use of visual representations in teaching and learning algebra. In this paper, we analyze the transformations from and to visual representations that were performed by 18 students (aged between 10 and 13) in a task designed to explore a figural pattern. The data were collected from an audio recording of the class, the students’ work, and the teacher’s notes about each lesson. The results confirm that visual representations are important. However, visual treatments of any kind of representation are decisive, since they give students other possibilities for seeing and understanding tasks, continuity and flexibility in their activities, and the ability to make conversions between representations. The creative realization of visual treatments is necessary, and the teacher has a significant role in helping students to learn how to do this.     

Empirical construction of decision procedures in stochastic morphology

Classification of signals with random forms is considered as a statistical hypothesis test problem. A method for empirical construction of decision procedures in statistical hypothesis test problems is proposed.     

模糊RBF神经网络在音频零水印中的应用

针对当前零水印不能"嵌入"有意义水印的不足,构建了在小波域中基于神经网络的零水印系统,提出了一种基于模糊RBF神经网络的音频零水印方案,有效解决了音频水印的鲁棒性与透明性之间的矛盾.模糊神经网络模糊系统的隶属度函数和推理规则决定RBF神经网络的结构和学习算法.因为水印方案不改变原始音频数据,所以具有良好的透明性,实验结果表明,方案具有很强的鲁棒性.     

Professionalism in Presentation

Communication to an audience can only be effected through either the audio or the visual senses. Thus, in any presentation, mastery of the technicalities involved in the effective use of audio-visual aids is of prime importance. Although such mastery cannot guarantee a good presentation, it can always guarantee to produce a better presentation than would have been the case without the use of such aids. This article discusses the techniques of good presentation.     

检验两个部分线性模型中非参函数相等

We propose the test statistic to check whether the nonparametric func-tions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.     

典型电磁现象的可视化实现

介绍了典型电磁现象的可视化实现过程.用计算机模拟计算出典型电磁现象在空间的分布情况,因此我们可以用图形方式来观察典型电磁现象.同时给出了几个具体实例.     

协整回归残量平稳性的小波检验

本文研究基于小波方法的协整回归残量平稳性检验。将文献[6]中的小波方法推广到了协整关系的检验,给出了对线性协整模型OLS回归后得到的残量进行平稳性检验的小波方法,得到了在原假设非协整下检验统计量的渐近分布。模拟实验和实例分析都验证了新方法的有效性。     

Generalized Cramér-von Mises tests of goodness of fit for doubly censored data

We generalize Cramér-von Mises statistics to test the goodness of fit of a lifetime distribution when the data are doubly censored. We derive the limiting distributions of our test statistics under the null hypothesis and the alternative hypothesis, respectively. We also give a strong consistent estimator for the asymptotic covariance of the self-consistent estimator for the survival function with doubly censored data. Thereby, a method, called the Fredholm Integral Equation method, is proposed to estimate the null distribution of test statistics. In this work, the perturbation theory for linear operators plays an important role, and some numerical examples are included.The author's research was supported by a Faculty Fellowship of University of Nebraska-Lincoln.     

一类相合的分位点型检验

广义非参数似然比检验统计量是一类很广的统计量,包含了众多重要的检验统计量,如Anderson-Darling(AD)等.利用Rubin的随机经验分布函数替代经验分布函数的方法,得到了广义非参数似然比检验统计量的新版本,构造了新的检验统计量.由于新的检验统计量在给定样本下仍然是随机变量,选择了它的分位点和期望作为检验统计量,分别称之为分位点型检验统计量和期望型检验统计量.在简单假设情况下,证明了分位点型检验统计量和期望型检验统计量在固定备择下的相合性.模拟结果显示,在某些备择下,新的检验的功效明显高于原有的基于经验分布函数的检验的功效.