一阶自回归模型参数变点的假设检验

本文讨论一阶自回归模型自回归参数$\phi$的变点问题. 对于一阶自回归模型, 在模型的白噪声序列的方差$\sigma^2$已知和未知的条件下, 利用最大似然方法, 我们分别讨论了模型自回归参数$\phi$的Abrupt Change-Point 和Gradual Change-Point的检测问题.     

The Unity Game–Reflections of a Faculty Moderate

Change is a perennial struggle for campuses. Trustees, presidents, policymakers, faculty, staff, students, alumni, and community groups all seek to alter some aspect of colleges and universities. Common wisdom is that higher education faculty, staff, and administrators do not want to change and are slow to innovate. This article examines the challenges of change from a macro perspective, using insights from studies of change and leadership, and the perspective of change agents, to provide a new hypothesis of why change is difficult: the presence of too many simultaneous and competing change initiatives, not the unwillingness of campus constituents to engage in change, prevent progress. Concentrated institutional action is impeded by too many stakeholders interested in different types of change, a lack of synergy among change initiatives, an inability to create priorities, leadership turnover, a pressure for leaders to innovate rather than implement, and the movement away from core institutional purposes in the pursuit of prestige.     

Technical change and the von Neumann coefficient of uniform expansion

We study technical change for multi-product technologies to examine its effect on economic growth for 27 OECD (Organization for Economic Cooperation and Development) countries during 1951–2014. We review the Malmquist index and reexamine von Neumann’s model of an expanding economy. We estimate the coefficient of uniform expansion via DEA (Data Envelopment Analysis) and use it to measure technical change via a Solow residual and an alternative von Neumann technical change index which equals the difference between the growth rates of the slowest growing output and the fastest growing input. We also exploit a property of constant returns to scale in order to examine technical change of the average technology. During 2005–2014 the Solow residual shows relatively fast technical change. In contrast, the Malmquist, average technology and alternative von Neumann technical change indexes show negative or stagnant technical change.     

Secondary mathematics teachers’ meanings for measure,slope, and rate of change

This article reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. The data was collected with a validated written instrument designed to diagnose teachers' mathematical meanings. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topic of targeted professional development.     

潜周期模型中频率变点的估计

本文用逐段计算周期图的办法研究了带有频率交点的潜周期模型估计问题，给出了交点数目、位置和潜频率的强相合估计．数值模拟表明本文方法对变点个数和潜频率估计很好，但是要准确估计交点位置需要较大样本量，估计对于噪声水平较高情况仍然有效。     

Modeling centralized organization of organizational change

Organizations change with the dynamics of the world. To enable organizations to change, certain structures and capabilities are needed. As all processes, a change process has an organization of its own. In this paper it is shown how within a formal organization modeling approach also organizational change processes can be modeled. A generic organization model (covering both organization structure and behavior) for organizational change is presented and formally evaluated for a case study. This model takes into account different phases in a change process considered in Organization Theory literature, such as unfreezing, movement and refreezing. Moreover, at the level of individuals, the internal beliefs and their changes are incorporated in the model. In addition, an internal mental model for (reflective) reasoning about expected role behavior is included in the organization model.     

时间序列多个突变点的贝叶斯推断——对我国GDP序列的实证分析

突变点的存在对经济分析与建模会产生重要影响."邹检验"仅仅在序列存在一个突变点时有效.为了对序列中可能存在的多个突变点进行判断,引入了基于贝叶斯推断的多个突变点判断理论,并将该理论应用于我国GDP序列中.笔者检测出该序列存在三个突变点,分别位于1961年,1976年,1989年.此外,发现加入合理的突变点后,模型的预测精度得到显著的提高.     

Malmquist生产率指数评析结果——技术变动的新诠释

为了判断创新活动是否有利于技术进步,预测技术变动的发展趋势,将Malmquist生产率指数评价结果进一步分解,挖掘技术变动的深层次知识,并将之应用于我国电子行业的技术创新活动分析。研究表明,运用经济学中的等产量曲线的分析原理,能够获取Malmquist生产率测算结果中技术变动指数各个构成部分所包含的管理信息,并可以判断决策单元的技术变动方向是否有利,最后对我国电子行业技术创新活动的实证研究发现我国电子行业创新活动总体上朝着有利于技术进步的方向发展。     

Change Trees and Mutagrams for the Visualization of Local Changes in Sequence Data

The analysis of local changes in sequence data is of interest for various applications such as the segmentation of DNA and other genetic sequences, or financial data sequences. Patterns of change that can be characterized as local jump change or slope change are of special interest. We propose simple graphical tools to visualize such patterns of local change. The concept of mode trees—developed for the visualization of local patterns in densities—is adapted to visualize patterns of local change in dependency on a threshold parameter by means of a change tree . The simultaneous visualization of scale effects, in analogy to SiZer, motivates another graphical device, the mutagram . We illustrate these concepts with several sets of sequence data.     

Moments of Change

There is a strong intuition that for a change to occur, there must be a moment at which the change is taking place. It will be demonstrated that there are no such moments of change, since no state the changing thing could be in at any moment would suffice to make that moment a moment of change. A moment in which the changing thing is simply in the state changed from or the state changed to cannot be the moment of change, since these states are respectively before and after the change; moreover, to select one of these moments over the other as the moment of change would be arbitrary. A moment in which the changing thing is neither in the state changed from nor in the state changed to cannot be the moment of change, since there are changes for which it is impossible for something to be in neither state. Finally, the moment of change cannot be a moment in which the changing thing is in both the state changed from and the state changed to, as suggested by Graham Priest and others. Even if, like proponents of this view, we are willing to accept the contradictions that the account entails, it is demonstrated that on such a model, every change would require an infinite number of other changes, every change would take an infinite amount of time, and some changes would occur without occurring at any time. Further, the model is grossly counterintuitive, with the exact nature of the counterintuitive element depending on what model of time and space one endorses. Finally, it is demonstrated that this model is incompatible with the Leibniz Continuity Condition.     

Simultaneous change point analysis and variable selection in a regression problem

In this paper, an information-based criterion is proposed for carrying out change point analysis and variable selection simultaneously in linear models with a possible change point. Under some weak conditions, this criterion is shown to be strongly consistent in the sense that with probability one, it chooses the smallest true model for large n. Its byproducts include strongly consistent estimates of the regression coefficients regardless if there is a change point. In case that there is a change point, its byproducts also include a strongly consistent estimate of the change point parameter. In addition, an algorithm is given which has significantly reduced the computation time needed by the proposed criterion for the same precision. Results from a simulation study are also presented.     

Weak signal detection in SPC

Changes in the behavior of dynamic systems are detected based on changes in the monitored quantities or their characteristics. This detection usually takes place by monitoring the time evolution of a variable and detecting the change at the time when a predetermined threshold is exceeded. This threshold is determined on the basis of the detection scheme requirements, in particular, the probability of false alarms and the detection rate for the actual change. In some cases, however, a change does not come suddenly, but certain “hints” in the system behavior can be observed that may indicate a future change. For example, an increasing frequency of outliers can result in a sudden permanent change in the signal. The occurrence of some “unusual” frequencies often indicates an imminent change. For example, an increasing correlation value indicates an undesired process status. Detection of these “subliminal” hints can often improve the characteristics of the detection scheme, especially the detection rate for the actual change. In this paper, we will deal with the detection of weak signals in statistical process monitoring using a control chart with adaptive control limits.     

On detection of change points using mean vectors

In this paper, the authors consider the problem of change points within the framework of model selection and propose a procedure for estimating the locations of change points when the number of change points is known. The strong consistency of this procedure is also established. The problem of detecting change points is discussed within the framework of the simultaneous test procedure. The case where the number of change points is unknown will be discussed in another paper.This project is supported by the National Natural Science Foundation of China and by the Air Office of Scientific Research of the United States.     

Base change for ≈SL2

Solvable base change for the metaplectic group ≈SL₂ over both local and global fields in studied. The method is to use Waldspurger's correspondence to relate base change for ≈SL₂ to base change for PGL₂. In the global case there are certain cuspidal representations which “disappear” under a quadratic base change. They then “reappear” under any subsequent quadratic base change. Such a phenomenon never occurs for PGL₂.     

Burgers方程的激波解与激波位置(英文)

讨论了Burgers方程激波解和位置的转移 .认为 :对该类方程 ,当边值发生微小变化时 ,不仅激波解发生变化 ,而且激波位置将发生较大的变化 ,甚至从内层移到边界 .其激波解也会发生相应的变化 .     

小波检测并估计非参函数变点

研究随机设计下非参函数变点的小波检测与估计问题.将小波方法与设计点转化方法相结合给出变点的检测统计量并研究检测的一致性.给出了变点个数和变点位置的估计量,证明了变点个数估计量的相合性并得到变点位置估计量的收敛速度.     

Bias of estimator of change point detected by a CUSUM procedure

For independent observations from a standard one-parameter exponential family, the estimator of change point after being detected by a CUSUM procedure is defined as the last zero point of the CUSUM process before the alarm time. By assuming that the change occurs far away from beginning and the control limit is large, an explicit form for the bias of estimator is derived conditioning on the change being detected. By further assuming that the change magnitude and its reference value approach zero at the same order, the local second order expansion of the bias is obtained for numerical evaluation. It is found that, surprisingly, even in the normal distribution case, the bias is non-zero when the change magnitude equals to its reference value, in contrast to the continuous time analog and the fixed sample size case. Numerical results show that the approximations are quite satisfactory.     

Solution representations of percentage change problems: the pre-service primary teachers’ mathematical thinking and reasoning

Solution representations can reveal how problem solvers communicate mathematical thinking and reasoning in problem-solving process. The present study examined the solution representations used by 20 pre-service teachers for the percentage change problems. The pre-service teachers were invited to solve a combination of simple and complex percentage change problems. The score for the majority of simple problems was 75% or above, but the score for the complex problems was below 75%. The highest percentage error occurred when the pre-service teachers encountered a percentage greater than 100% in the percentage change problems. Irrespective of their level of mathematics qualifications, the equation approach demonstrating two-step problem-solving process was the predominant strategy adopted by the pre-service teachers. The equation approach imposes low cognitive load and, therefore, is more accessible and efficient than the unitary approach. A few pre-service teachers used the unitary approach. The findings indicate that the pre-service teachers possessed relevant mathematical knowledge for percentage change problems. Furthermore, the inclusion of the equation approach in mathematics textbooks would provide an alternative perspective regarding the teaching and learning of percentage change problems.     

The Bayesian Change Point and Variable Selection Algorithm: Application to the δ18O Proxy Record of the Plio-Pleistocene

In this article, we introduce the Bayesian change point and variable selection algorithm that uses dynamic programming recursions to draw direct samples from a very high-dimensional space in a computationally efficient manner, and apply this algorithm to a geoscience problem that concerns the Earth's history of glaciation. Strong evidence exists for at least two changes in the behavior of the Earth's glaciers over the last five million years. Around 2.7 Ma, the extent of glacial cover on the Earth increased, but the frequency of glacial melting events remained constant at 41 kyr. A more dramatic change occurred around 1 Ma. For over three decades, the “Mid-Pleistocene Transition” has been described in the geoscience literature not only by a further increase in the magnitude of glacial cover, but also as the dividing point between the 41 kyr and the 100 kyr glacial worlds. Given such striking changes in the glacial record, it is clear that a model whose parameters can change through time is essential for the analysis of these data. The Bayesian change point algorithm provides a probabilistic solution to a data segmentation problem, while the exact Bayesian inference in regression procedure performs variable selection within each regime delineated by the change points. Together, they can model a time series in which the predictor variables as well as the parameters of the model are allowed to change with time. Our algorithm allows one to simultaneously perform variable selection and change point analysis in a computationally efficient manner. Supplementary materials including MATLAB code for the Bayesian change point and variable selection algorithm and the datasets described in this article are available online or by contacting the first author.     

关于只有一个变点模型的非参数推断

这里 μ(t)为非随机函数,μ′(t)为 μ(t)的导函数,α,θ.为未知常数,0相似文献