多元对应分析在抽样调查分析中的应用

本文应用多元对应分析、聚类分析等数理统计方法 ,对抽样调查问卷进行分析 ,从而得出各类读者群的特征及它们之间的差异     

The exploratory analysis of qualitative variables by means of three-way analysis of two types of quantification matrices

A comparison is made between a number of techniques for the exploratory analysis of qualitative variables. The paper mainly focuses on a comparison between multiple correspondence analysis (MCA) and Gower's principal co-ordinates analysis (PCO), applied to qualitative variables. The main difference between these methods is in how they deal with infrequent categories. It is demonstrated that MCA solutions can be dominated by infrequent categories, and that, especially in such cases, PCO is a useful alternative to MCA, because it tends to downweight the influence of infrequent categories. Apart from studying the difference between MCA and PCO, other alternatives for the analysis of qualitative variables are discussed, and compared to MCA and PCO.     

Log-linear parameterizations in discriminant analysis

Applications of log-linear models in discrete discriminant analysis usually treat the grouping variable as a variable in the model. An alternative parameterization is introduced which models the association structure between variables for each population separately. The separate log-linear models may have differing complexity. It is shown that these approaches lead to different classes of models. Applications to the choice of car brand and credit scoring show the usefulness of separate modelling.     

The structured total least‐squares approach for non‐linearly structured matrices

In this paper, an extension of the structured total least‐squares (STLS) approach for non‐linearly structured matrices is presented in the so‐called ‘Riemannian singular value decomposition’ (RiSVD) framework. It is shown that this type of STLS problem can be solved by solving a set of Riemannian SVD equations. For small perturbations the problem can be reformulated into finding the smallest singular value and the corresponding right singular vector of this Riemannian SVD. A heuristic algorithm is proposed. Some examples of Vandermonde‐type matrices are used to demonstrate the improved accuracy of the obtained parameter estimator when compared to other methods such as least squares (LS) or total least squares (TLS). Copyright © 2002 John Wiley & Sons, Ltd.     

Profiting from correlations: Adjusted estimators for categorical data

To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the estimation. Studying contingency tables, estimators for marginal distributions are proposed under the assumption that another marginal is known. It is shown that the weighted estimators have a strictly smaller asymptotic variance whenever the two marginals are correlated. The finite sample performance is illustrated in a simulation study. As an application to traffic accident data the method allows for correcting a well‐known bias in the observed injury severity distribution.     

列联资料的有向聚类分析及其应用

本文针对单向有序列联资料 ,提出了有序因素的秩效应概念。在秩效应排序的基础上 ,构造了平均秩效应原则 ,并对因素各水平进行有向聚类分析。利用该方法对大学生隐性教育调查资料进行了剖析     

Spline methods for the solution of hyperbolic equation with variable coefficients

In this study, we developed the methods based on nonpolynomial cubic spline for numerical solution of second‐order nonhomogeneous hyperbolic partial differential equation. Using nonpolynomial cubic spline in space and finite difference in time directions, we obtained the implicit three level methods of O(k² + h²) and O(k² + h⁴). The proposed methods are applicable to the problems having singularity at x = 0, too. Stability analysis of the presented methods have been carried out. The presented methods are applied to the nonhomogeneous examples of different types. Numerical comparison with Mohanty's method (Mohanty, Appl Math Comput, 165 (2005), 229–236) shows the superiority of our presented schemes. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A simple diagonals-parameter symmetry and quasi-symmetry model

Goodman (1979) proposed a class of diagonals-parameter symmetry models for square contingency tables with ordered categories, A simple version of that model is considered in which the log odds parameters have a linear pattern. The model is also a simple quasi-symmetry model. It fits well when there is an underlying bivariate normal distribution.     

列联表分析及在SPSS中的实现

本文首先介绍了列联表的一致性与独立性检验、相关分析、某些特殊统计量等内容 ,然后说明了上述分析在SPSS9.0中的实现 ,并最终结合实例进行了应用     

Stability analysis of tree structured decision functions

In multicriteria decision problems many values must be assigned, such as the importance of the different criteria and the values of the alternatives with respect to subjective criteria. Since these assignments are approximate, it is very important to analyze the sensitivity of results when small modifications of the assignments are made. When solving a multicriteria decision problem, it is desirable to choose a decision function that leads to a solution as stable as possible. We propose here a method based on genetic programming that produces better decision functions than the commonly used ones. The theoretical expectations are validated by case studies.     

Non‐standard analysis in ACA0 and Riemann mapping theorem

This research is motivated by the program of reverse mathematics and non‐standard arguments in second‐order arithmetic. Within a weak subsystem of second‐order arithmetic ACA₀, we investigate some aspects of non‐standard analysis related to sequential compactness. Then, using arguments of non‐standard analysis, we show the equivalence of the Riemann mapping theorem and ACA₀ over WKL₀. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Models of multi-dimensional analysis for qualitative data and its application

Online analytical processing (OLAP) is one of the technologies that enable client applications to efficiently access data multi-dimensionally. This powerful tool helps users create new views of data, based on a rich array of ad hoc calculation functions. However, the complexity of queries required to support OLAP applications in the multi-dimensional model makes OLAP difficult to implement by simply using standard relational database technology in a static manner. Moreover, OLAP requires numerical data input. In contrast, qualitative data cannot be operated on using OLAP technique. This paper develops models of multi-dimensional analysis, based on traditional multi-dimensional techniques and OLAP techniques to analyze qualitative data dynamically. The models are able to discover the kernel knowledge from the current formulated knowledge. The proposed model is used to develop multi-dimensional algebra to facilitate operation in data warehouse.     

一类具功能反应的食饵-捕食者系统的定性分析

运用微分方程定性与稳定性分析的方法研究了一类食饵-捕食者系统的定性行为,讨论了该系统的平衡点的性态,给出了该系统极限环不存在性存在性的充分条件以及至多存在一个极限环的充分条件,从而补充和推广了前人已有的结果.     

Stability and convergence of the mark and cell finite difference scheme for Darcy‐Stokes‐Brinkman equations on non‐uniform grids

In this paper, we consider the mark and cell (MAC) method for Darcy‐Stokes‐Brinkman equations and analyze the stability and convergence of the method on nonuniform grids. Firstly, to obtain the stability for both velocity and pressure, we establish the discrete inf‐sup condition. Then we introduce an auxiliary function depending on the velocity and discretizing parameters to analyze the super‐convergence. Finally, we obtain the second‐order convergence in L2 norm for both velocity and pressure for the MAC scheme, when the perturbation parameter ? is not approaching 0. We also obtain the second‐order convergence for some terms of ∥·∥_? norm of the velocity, and the other terms of ∥·∥_? norm are second‐order convergence on uniform grid. Numerical experiments are carried out to verify the theoretical results.     

Stability of efficiency evaluations in data envelopment analysis

Efficiency evaluations in data envelopment analysis are shown to be stable for arbitrary perturbations in the convex hulls of input and output data. Also, the corresponding restricted Lagrange multiplier functions are shown to be continuous. The results are proved using point-to-set mappings and a particular region of stability from input optimization.Research partly supported by National Science Foundation Grants, Office of Naval Research Grant, and by the Natural Sciences and Engineering Council of Canada.     

Benefit-cost analysis using data envelopment analysis

Benefit-cost analysis is required by law and regulation throughout the federal government. Robert Dorfman (1996) declares ‘Three prominent shortcomings of benefit-cost analysis as currently practiced are (1) it does not identify the population segments that the proposed measure benefits or harms (2) it attempts to reduce all comparisons to a single dimension, generally dollars and cents and (3) it conceals the degree of inaccuracy or uncertainty in its estimates.’ The paper develops an approach for conducting benefit-cost analysis derived from data envelopment analysis (DEA) that overcomes each of Dorfman's objections. The models and methodology proposed give decision makers a tool for evaluating alternative policies and projects where there are multiple constituencies who may have conflicting perspectives. This method incorporates multiple incommensurate attributes while allowing for measures of uncertainty. An application is used to illustrate the method. This work was funded by grant N00014-99-1-0719 from the Office of Naval Research     

Delay analysis of discrete-time priority queue with structured inputs

This paper investigates a discrete-time priority queue with multi-class customers. Applying a delay-cycle analysis, we explicitly derive the probability generating function of the waiting time for an individual class in a geometric batch input queue under preemptive-resume and head-of-the-line priority rules. The conservation law and waiting time characterization for a general class of discrete-time queues are also presented. The results in this paper cover several previous results as special cases.     

Global qualitative analysis of a discrete host‐parasitoid model with refuge and strong Allee effects

In this paper, we discuss the qualitative behavior of a discrete host‐parasitoid model with the host subject to refuge and strong Allee effects. More precisely, we study the local and global asymptotic stability, stable manifolds and unstable manifolds of boundary equilibrium points, existence and unique positive equilibrium point, local and global behavior of the positive equilibrium point, and the uniform persistence for the model with the host subject to the refuge or both refuge and strong Allee effects. It is also proved that the model undergoes a transcritical bifurcation in a small neighborhood of the boundary equilibrium point. Some numerical simulations are given to support our theoretical results. We can obtain that the addition of the refuge may make the parasitoids go extinct while the hosts survive or may stabilize the host‐parasitoid interaction; the addition of both refuge and strong Allee effects has either a negative or positive impact on the coexistence of both populations.     

Global dynamics of an age‐structured virus model with saturation effects

An infection‐age virus dynamics model for human immunodeficiency virus (or hepatitis B virus) infections with saturation effects of infection rate and immune response is investigated in this paper. It is shown that the global dynamics of the model is completely determined by two critical values R ₀, the basic reproductive number for viral infection, and R ₁, the viral reproductive number at the immune‐free infection steady state (R ₁<R ₀). If R ₀<1, the uninfected steady state E ⁰ is globally asymptotically stable; if R ₀>1 > R ₁, the immune‐free infected steady state E ^? is globally asymptotically stable; while if R ₁>1, the antibody immune infected steady state is globally asymptotically stable. Moreover, our results show that ignoring the saturation effects of antibody immune response or infection rate will result in an overestimate of the antibody immune reproductive number. Copyright © 2016 John Wiley & Sons, Ltd.     

Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables

In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.