非参数自回归模型异方差的小波检验

本文讨论了非参数自回归模型异方差的检验问题.在非参数自回归模型的建模过程中,通常假定方差为常数.然而在建模前,我们应该首先检验这-假定是否成立.本文将利用小波方法来检验异方差问题.我们首先利用核估计方法定义经验小波系数,然后讨论其渐近性质.在此基础上,我们提出了异方差性检验的统计量.数值模拟结果表明,我们的方法表现良好.     

随机权函数半参数回归模型的导方差统计分析

在回归分析中,观测值的方差齐性只是一个基本的假定,在参数、半参数和非参数回归模型中关于异方差检验和估计问题已有很多研究.本文在冉昊和朱忠义(2004)讨论的半参数回归模型的基础上,用随机参数方法,讨论随机权函数半参数回归模型中的异方差检验问题,得到了方差齐性检验Score统计量,同时,当半参数模型存在异方差时,本文还给出了估计方差的方法.     

具有结构变化的非线性回归模型的阶段异方差检验

对于具有结构变化的非线性回归模型,两阶段的随机误差同时具有方差齐性是一个基本假设,但是该假设未必正确．本文研究该模型阶段异方差的检验问题．首先探讨了两阶段异方差的同时检验,然后构造了两阶段异方差的两个单个检验,分别得到了同时检验和单个检验的score统计量以及相应的调整形式．然后应用得到的检验统计量分析了南澳大利亚洋葱数据的阶段异方差性(Ratkowsky,1983),并用AIC,SBC进行模型比较,得到的结果与检验结果非常吻合．最后,用Monte Carlo模拟方法研究了统计量的检验功效．     

广义p-值与panel数据模型的精确检验

在panel模型中,如果方差分量已知,对回归系数的检验,存在一致最优功效检验.但往往方差分量未知,这时采用的方法就是用它们的估计代替它们.不同的方差分量的估计,就得到不同的检验统计量.这些检验统计量的分布都是未知的,在小样本情况下,很难控制它们的检验水平.本文采用广义p值的方法,给出了一种精确的检验.模拟结果显示,这种检验能很好的控制检验水平,并且有更高的检验功效.同时,本文利用广义置信域的方法给出了回归系数的广义置信球.     

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在广义参数和非参数模型中, 虽然不存在异方差检验问题, 但是方差成分的检验问题仍是研究者们关心的对象. 本文利用P-样条的方法, 研究了广义单指标混合模型的方差成分检验问题. 得到了检验广义单指标混合模型是否存在由随机效应引起的偏大离差问题的Score检验统计量, 最后给出计算机模拟的例子, 证实了文中所提出方法的可行性和有效性, 推广和发展了先前的研究工作     

具有ARIMA（0，1，0）对称误差的非线性模型的统计诊断

本文讨论具有ARIMA(0,1,0)对称误差的非线性模型的异方差检验和局部影响分析.对称误差分布族包括正态,t,power exponential,logistics Ⅰ,Ⅱ,污染正态等所有对称连续分布.文章首先导出了关于白噪声异方差检验的score统计量及其调整形式,然后对模型进行了局部影响分析,得到了基于似然函数扰动和反应变量扰动的诊断统计量.最后,利用实际数据说明了检验方法的应用,并用Monte Carlo模拟方法研究了异方差检验统计量的检验功效.     

具有AR(1)误差的线性随机效应模型中方差齐性和自相关性的检验

在回归分析中，方差齐性是一个很基本的假设．本文对具有AR(1)误差的线性随机效应模型，研究了方差齐性和自相关性的检验问题．我们分别讨论了随机误差异方差、随机效应异方差、多元异方差以及自相关性的检验问题，并用score检验方法给出了三种方差齐性和自相关性的检验统计量．随机模拟的结果表明，当样本容量较大时，检验的功效较好．本文还给出一个数值例子说明检验方法的实用性．另外，模型的结果也可以推广到非线性情形．     

非参数回归中方差变点的小波检测(英文)

本文主要研究了非参数回归模型中方差函数的变点, 利用小波方法构造的检验量来检测方差中的变点,建立了这些检验量的渐近分布, 并且运用这些检验量构造了方差变点的位置和跳跃幅度的估计, 给出了这些估计的渐近性质, 并进一步通过随机模拟验证了本文方法在有限样本下的性质.     

单指标模型异方差检验（英文）

在可加回归模型中,高维回归分析一般采用单指标模型.该模型与参数模型相比更加灵活,同时避免了维数灾难,因为单指标将标准变量向量的维数降低为单变量指标.本文构建了一个带有函数型误差项的单指数回归模型用于检验单指标模型的异方差性.由于回归模型的有效推断要求在存在异方差的情况下考虑异方差,本文提出了检验单指标模型方差不变性的假设.将Levene检验和无限因子水平的方差分析理论结合得到检验统计量用来评估方差同质性.模拟研究显示与已有方法相比,所提检验统计量适用于多种情形.最后将本文的方法应用于分析一组实际数据.     

非线性随机效应模型的异方差性检验

随机效应模型广泛应用于刻画重复测量数据的特征．在该模型中,随机误差的方差包括受试群体内部及受试群体之间两项方差．Ｚｈａｎｇ和 Ｗｅｉｓｓ ２０００年研究了线性随机效应模型的异方差检验,本文对非线性随机效应模型,分别讨论了群体内、群体间和多变量的异方差性的检验问题,得到了检验的ｓｃｏｒｅ统计量,并讨论了三种情形下,相应的ｓｃｏｒｅ函数之间的关系．最后给出一个数值例子说明上述方法的有用性．     

The Place of Logic in Reasoning

Reasoning is a goal-oriented activity. The logical steps are at best the median part of a full reasoning: before them, a language has to be defined, and a model of the goal in this language has to be developed; after them, their result has to be checked in the real world with respect to the goal. Both the prior and the subsequent steps can be conducted rationally; none of them has a logical counterpart. Furthermore, Logic aims at prescribing what a correct reasoning is. But correct with respect to what? If the answer is: with respect to truth, the next question is whether the truth in everyday life, physics, economy, is the same as the truth that logicians have in mind. Resorting to Logic is justified only if an idealization in terms of true propositions in the logical sense is compatible with the goal. If such an idealization is legitimate, so is the use of classical Logic. If not, there is no authority forbidding to skew Logic in order to better reflect the nature of the reasoning required for the task.     

Operational Research and Innovation in Management Methods

This paper is an attempt to specify some of the conditions which would need to be met both in the staffing of a group and in its place in the organization, if operational research is to play a part in initiating change in the processes of decision-making. An analogy is drawn with the "planned change" of the behavioural sciences.The conflict inherent in the role is identified. To illustrate the kinds of insights the group would need to possess, into the structure of an organization, and the ways its control systems operate, examples of long-, medium- and short-term decision-making are given.Finally, an attempt is made to identify the characteristics which the group would need to possess for success in this innovative role, including its knowledge, attitudes and insights. The relationship between the group and the sponsor of work is discussed, and between the group and the parent organization in general. It is suggested that a participative style of organization would be the most appropriate for effective innovation in the methods of management by this means.     

The determination of two moving heat sources in two-dimensional inverse heat problem

There are some restrictions in the estimation of location and strength problems in recent studies. One of the restrictions is that the problem is limited to the static sources and the single moving source. In other words, there is no method available to estimate the location and the strength of two moving sources presently. Therefore, it is necessary to develop a robust method to estimate the location and the strength of two moving heat sources. In this paper, a numerical algorithm is proposed to determine the problem sequentially. Special feature about this method is that no preselect functional form for the unknown sources is necessary and no sensitivity analysis is needed in the algorithm. Two examples are used to demonstrate the characteristics of the proposed method. From the results, they show that the proposed method is an accurate and efficient method to determine the location and the strength of two moving sources in the inverse heat conduction problem.     

Development of generalized Iwan model to simulate frictional contacts with variable normal loads

Most friction models are originally proposed to predict restoring forces in mechanical contacts with constant normal load. In practice the contact interface kinematics may involve normal motion in addition to the tangential displacements, leading to variation of the contact normal load. This phenomenon is observed most strongly in contacts with high lateral vibration amplitudes and is known as slap. The current study establishes a general friction model to account for variation in the normal load and enables one to predict the behavior of a contact more precisely. Iwan model (1966) [5] is a suitable candidate for contact interface modeling and is able to represent the stick-micro/macro slip behavior involved in a friction contact. This physical based model is employed in the current work and its physical parameters are generalized to include the normal load variation effects. The model is characterized by a slippage distribution density function and a linear stiffness at stick state. Both these parameters, defined in presence of constant normal load in the original model, are derived considering normal load variation leading to generalization of the contact model. Conventional models with constant normal loads produce symmetric contact interface hysteresis loops, but the developed generalized Iwan model is capable of generating asymmetric hysteresis loops similar to those frequently seen in experiments. The generalized contact model is employed to simulate the measured behavior of a beam with frictional support observed in an experimental test set-up. The contact slippage distribution function is first identified in a constant normal load condition. Next in low levels of contact preloads where variation of the normal load is significant, the identified distribution function in generalized form is employed to predict the experimental observations.     

Perspectives sur les recherches en didactique des mathématiques

The paper is a review of chosen approaches to research in mathematics education in several countries: Germany, France, United States, Russia, Poland, Canada. The review is done in the literary form of a satire, in which a character is taken on a voyage to a variety of “islands” respresenting different research interests and methodologies in mathematics education. The story is a parody of Homer’sOdyssee, and the main character is called Odysseus. Odysseus’ role is played by the famous arithmetic problem about a team of an unknown number of scythers who are given the task of scything two meadows one of which is double the size of the other. As the problem travels from one “island” to another, mathematics educators do different things to and with the problem and it is solved is a variety of ways. The main text of the paper reads as a story and there are no explicit references and names of authors, whose work is only alluded to. However, the solution to all allusions, i.e. explicit references, can be found in the footnotes.     

加权和法在Vague集中的应用

针对应用广泛的加权和法的特征,研究在Vague集中应用加权和法,提出了在Vague集中应用加权和的方法,并通过实际算例验证了此方法的有效性.     

Bayesian lasso binary quantile regression

In this paper, a Bayesian hierarchical model for variable selection and estimation in the context of binary quantile regression is proposed. Existing approaches to variable selection in a binary classification context are sensitive to outliers, heteroskedasticity or other anomalies of the latent response. The method proposed in this study overcomes these problems in an attractive and straightforward way. A Laplace likelihood and Laplace priors for the regression parameters are proposed and estimated with Bayesian Markov Chain Monte Carlo. The resulting model is equivalent to the frequentist lasso procedure. A conceptional result is that by doing so, the binary regression model is moved from a Gaussian to a full Laplacian framework without sacrificing much computational efficiency. In addition, an efficient Gibbs sampler to estimate the model parameters is proposed that is superior to the Metropolis algorithm that is used in previous studies on Bayesian binary quantile regression. Both the simulation studies and the real data analysis indicate that the proposed method performs well in comparison to the other methods. Moreover, as the base model is binary quantile regression, a much more detailed insight in the effects of the covariates is provided by the approach. An implementation of the lasso procedure for binary quantile regression models is available in the R-package bayesQR.     

Computational error analysis of periodic solutions for singular semilinear parabolic problems

By using the monotone method, a theoretical and computational method is given to find, to the degree of accuracy desired, approximate solutions of a class of singular semilinear parabolic problems. So that the error between the actual solution and its approximation is within a given error tolerance, the number of iterations is determined. Since each iterate is in terms of an infinite series, the number of terms to be retained in each iterate is determined so that its error from the exact iterate is within a given error tolerance. An improved rate of convergence is then given to show that it is possible to reduce the number of terms retained in each iterate. An algorithm is also described to obtain numerical solutions. For illustration of the computational methods developed, a numerical example is given.     

精确覆盖问题的加权分治算法

精确覆盖问题是组合优化中经典的NP-Hard问题之一,其在诸多领域具有广泛的应用价值。本文首先研究了精确覆盖问题的数学性质,并根据数学性质提出相应的分支降阶规则以缩小问题的规模;接着设计了一个基于分支降阶的回溯算法求解该问题;然后运用常规技术分析得出该精确算法的时间复杂度为O(1.4656^k);最后运用加权分治技术对该算法的时间复杂度进行分析,将该算法的时间复杂度降为O(1.3842^k)。文章最后通过一个示例进一步阐述该算法的原理,并与其他精确算法进行了对比分析,研究结果表明该算法是可行的,也是有效的。     

Fourier–Bessel theory on flow acoustics in inviscid shear pipeline fluid flow

Flow acoustics in pipeline is of considerable interest in both industrial application and scientific research. While well-known analytical solutions exist for stationary and uniform mean flow, only numerical solutions exist for shear mean flow. Based on potential theory, a general mathematical formulation of flow acoustics in inviscid fluid with shear mean flow is deduced, resulting in a set of two second-order differential equations. According to Fourier–Bessel theory which is orthogonal and complete in Lebesgue Space, a solution is proposed to transform the differential equations to linear homogeneous algebraic equations. Consequently, the axial wave number is numerically calculated due to the existence condition of non-trivial solution to homogeneous linear algebraic equations, leading to the vanishment of the corresponding determinant. Based on the proposed method, wave propagation in laminar and turbulent flow is numerically analyzed.