基于核主成分分析和加权聚类分析的综合评价方法

针对传统主成分分析在处理非线性问题上的不足,文章阐述了应用核主成分分析进行数据处理的改进方法,并介绍了一种基于核主成分的加权聚类分析的综合评价方法.实验表明,该方法可以改进传统的综合评价方法.     

线性无量纲化方法的性质分析

内容提要：在对多种线性无量纲化方法特点分析的基础上,给出了“理想无量纲化方法”应该满足的一些性质,并证明了“理想无量纲化方法不存在”的结论。提出了“构建逼近理想性质的复合无量纲化方法”的思路,并构造了一种优良的复合无量纲化方法——“极标复合法”。提出了指标无量纲化过程的稳定性问题,着重分析造成结果不稳定的“指标数据分布”方面的原因,并给出了一种针对线性无量纲化方法的改进型。     

评价指标的非线性无量纲模糊处理方法

文章阐述了评价指标无量纲处理在综合评价中的重要作用，针对目前评价实践中存在的问题，运用指数函数和模糊数学的有关知识和方法，提出了适用于现行多数评价指标的一种非线性无量纲模糊处理方法。文中介绍了处理模型应具备的性质，分别就正指标、逆指标和适度指标给出了其相应的非线性模糊量化模型及模型中标准值的确定方法     

基于协方差函数的非线性主成分分析

一、引言 主成分分析(Principal Component Analysis,PCA)是最为常用的特征提取方法,被广泛应用到各领域,如模式识别、图像处理、综合评价、故障诊断等.它通过对原始数据的加工处理,简化问题处理的难度并提高数据信息的信噪比,以改善抗干扰能力.然而,从本质上讲主成分分析方法是一种线性映射方法,在处理非线性问题时,往往不能取得好的效果.     

也谈主坐标分析法在企业综合评估中的运用

南京经济学院的马伯仁同志在《主坐标分析法在企业评估中的运用》一文中提出了采用主坐标分析法对企业进行综合评估 ,这是一次有益的尝试 ,为多指标综合评价提供了一种新的思路 ,但忽略了应用条件。本文拟对主坐标分析法在企业综合评估中的应用问题提出一些看法 ,兼与马伯仁同志商榷。１．在综合评价排序时 ,主坐标分析法不如主成分分析法直观。主坐标分析法中对样品之间距离的抽象测度 ,最常用的是欧氏距离和绝对距离。理论上已经证明 :主坐标分析法的欧氏距离若是从标准化数据出发计算 ,则结果与Ｒ型主成分分析相同 ;若是从其它无量纲化数…     

基于正态分布点值化的区间主成分评价法及应用

针对区间数据点值化过程中所存在的“代表性不足”的缺陷,提出了基于正态分布的点值化方法并将之应用于区间主成分评价法。通过与基于中心点值化的区间主成分法的比较,得到三个主要结论：第一,基于正态分布的点值化方法能将各样品的点值化结果导向指标均值,而非区间值的中心点;第二,基于正态分布的点值化结果增加了数据信息量;第三,基于正态分布点值化的区间主成分评价法提高了数据降维效果,具有更好的因子命名能力。应用结果表明,在考虑正态分布情况下,对区间数据的点值化处理方法具有较好的效果,基于正态分布点值化的方法可推广至基于区间数的评价和决策问题。     

线性无量纲化方法比较研究

根据线性无量纲化方法函数构成所使用的中心点值和值域指标以及其斜率和截距的表达式,对8种线性无量纲化方法进行分析,从不同的角度再次论证不同线性无量纲化方法所满足的性质定理,并进行了理论论证。同时,通过对线性无量纲化方法的分类比较,结合相关性质定理提出了多种线性无量纲化方法,并说明了其相关性质,具有一定的科学性。同时还分析了在对多指标数据进行综合评价的过程中只采用一种线性无量纲化方法的不足,提出了采用多种无量纲化方法的设想的理论可行性,并用案例进行了实证分析,表明其存在一定的合理性。     

一种具有奖惩特征的动态主成分综合评价法

由于利用主成分进行综合评价时，一般是基于当期的截面数据而获得的评价结果，没有考虑到上一期情况的影响，因此该方法为一种静态的综合评价方法。针对这一方面的不足，本文设计了根据主成分分析法得出的主成分综合得分，引入一种奖惩因子将其主成分综合得分转换为主成分排序指数，从而形成了以主成分排序指数为评价依据的动态主成分综合评价法。     

基于Lasso改进的一般因果关系检验

通常所说的Granger因果关系检验，实际上是对线性因果关系的检验，无法检验非线性因果关系。Peguin和Terasvirta（1999）进行了基于泰勒展式的一般性扩展，应用于非线性因果关系检验，并采用提取主成分的方法解决其中的多重共线性问题。但是，提取主成分对解决多重共线性的效果并不太好。Lasso回归是目前处理多重共线性的主要方法之一，相对于其他方法，更容易产生稀疏解，在参数估计的同时实现变量选择，因而可以用来解决检验中的多重共线性问题，以提高检验的效率。对检验程序的模拟结果表明，基于Lasso回归的检验取得较好的效果。     

基于高维数据的改进CCC-GARCH模型的估计及应用

高维数据给传统的协方差阵估计方法带来了巨大的挑战,数据维度和噪声的影响使传统的CCCGARCH模型估计起来较为困难。将主成分和门限方法有效结合,应用到CCC-GARCH模型的估计中,提出基于主成分正交补门限方法的CCC-GARCH模型(PTCCC-GARCH)。PTCCC模型主要通过前K个最优主成分来刻画大维协方差阵的信息,并通过门限函数以剔除噪声的影响。通过模拟和实证研究发现:较CCCGARCH模型而言,PTCCC-GARCH模型明显提高了高维协方差阵的估计和预测效率;并且将其应用在投资组合时,投资者获得了更高的投资收益和经济福利。     

Clustering of gamma-ray bursts through kernel principal component analysis

We consider the problem related to clustering of gamma-ray bursts (from “BATSE” catalogue) through kernel principal component analysis in which our proposed kernel outperforms results of other competent kernels in terms of clustering accuracy and we obtain three physically interpretable groups of gamma-ray bursts. The effectivity of the suggested kernel in combination with kernel principal component analysis in revealing natural clusters in noisy and nonlinear data while reducing the dimension of the data is also explored in two simulated data sets.     

Estimation on semi-functional linear errors-in-variables models

Abstract

Semi-functional linear regression models are important in practice. In this paper, their estimation is discussed when function-valued and real-valued random variables are all measured with additive error. By means of functional principal component analysis and kernel smoothing techniques, the estimators of the slope function and the non parametric component are obtained. To account for errors in variables, deconvolution is involved in the construction of a new class of kernel estimators. The convergence rates of the estimators of the unknown slope function and non parametric component are established under suitable norm and conditions. Simulation studies are conducted to illustrate the finite sample performance of our method.     

Exploring the variability of DNA molecules via principal geodesic analysis on the shape space

Most of the linear statistics deal with data lying in a Euclidean space. However, there are many examples, such as DNA molecule topological structures, in which the initial or the transformed data lie in a non-Euclidean space. To get a measure of variability in these situations, the principal component analysis (PCA) is usually performed on a Euclidean tangent space as it cannot be directly implemented on a non-Euclidean space. Instead, principal geodesic analysis (PGA) is a new tool that provides a measure of variability for nonlinear statistics. In this paper, the performance of this new tool is compared with that of the PCA using a real data set representing a DNA molecular structure. It is shown that due to the nonlinearity of space, the PGA explains more variability of the data than the PCA.     

A Note on Unwanted Variance in Exploratory Factor Models

One strategy of exploratory factor analysis is to decide on the number of factors to extract by means of the eigenvalues of an initial principal component analysis. The present article proves that there is a non zero covariance of the factors with the components rejected when the number of factors to extract is determined by means of principal components analysis. Thus, some of the variance declared as irrelevant or unwanted in an initial principal component analysis is again part of the final factor model.     

基于非线性-主成分Logistic回归的会计舞弊识别研究

混沌理论认为,人类行为大多具有非线性特征。会计舞弊属于行为会计的研究范畴,而传统上基于统计理论构建的舞弊识别模型大多受限于线性约束假设,可能存在模型设定偏误和信息提取不充分的缺陷。以沪深A股受到监管处罚的上市公司及其配对公司为样本,借鉴Taylor展开式的非线性思想,并使用主成分分析消除变量多重共线性,构建了非线性-主成分Logistic回归的会计舞弊识别模型。与线性回归模型对比发现,前者具有更高的舞弊识别正确率,模型拟合度更优。应用这一模型有助于更加充分提取舞弊识别信息,提高舞弊识别效率。     

ADE-4: a multivariate analysis and graphical display software

We present ADE-4, a multivariate analysis and graphical display software. Multivariate analysis methods available in ADE-4 include usual one-table methods like principal component analysis and correspondence analysis, spatial data analysis methods (using a total variance decomposition into local and global components, analogous to Moran and Geary indices), discriminant analysis and within/between groups analyses, many linear regression methods including lowess and polynomial regression, multiple and PLS (partial least squares) regression and orthogonal regression (principal component regression), projection methods like principal component analysis on instrumental variables, canonical correspondence analysis and many other variants, coinertia analysis and the RLQ method, and several three-way table (k-table) analysis methods. Graphical display techniques include an automatic collection of elementary graphics corresponding to groups of rows or to columns in the data table, thus providing a very efficient way for automatic k-table graphics and geographical mapping options. A dynamic graphic module allows interactive operations like searching, zooming, selection of points, and display of data values on factor maps. The user interface is simple and homogeneous among all the programs; this contributes to making the use of ADE-4 very easy for non- specialists in statistics, data analysis or computer science.     

A non linear analysis of the preference for preservation of the teeth

Data resulting from behavioral dental research, usually categorical or discretized and having unknown measurement and distributional characteristics, often cannot be analyzed with classical multivariate techniques. A non linear principal components technique called multiple correspondence analysis is presented with its corresponding computer program that can handle this kind of data. The model is described as a form of multidimensional scaling. The technique Is applied in order to establish which factors are associated with an Individual's preference for preservation of the teeth.     

Functional Modelling and Classification of Longitudinal Data*

Abstract. We review and extend some statistical tools that have proved useful for analysing functional data. Functional data analysis primarily is designed for the analysis of random trajectories and infinite‐dimensional data, and there exists a need for the development of adequate statistical estimation and inference techniques. While this field is in flux, some methods have proven useful. These include warping methods, functional principal component analysis, and conditioning under Gaussian assumptions for the case of sparse data. The latter is a recent development that may provide a bridge between functional and more classical longitudinal data analysis. Besides presenting a brief review of functional principal components and functional regression, we develop some concepts for estimating functional principal component scores in the sparse situation. An extension of the so‐called generalized functional linear model to the case of sparse longitudinal predictors is proposed. This extension includes functional binary regression models for longitudinal data and is illustrated with data on primary biliary cirrhosis.     

Dynamic principal component analysis with missing values

Dynamic principal component analysis (DPCA), also known as frequency domain principal component analysis, has been developed by Brillinger [Time Series: Data Analysis and Theory, Vol. 36, SIAM, 1981] to decompose multivariate time-series data into a few principal component series. A primary advantage of DPCA is its capability of extracting essential components from the data by reflecting the serial dependence of them. It is also used to estimate the common component in a dynamic factor model, which is frequently used in econometrics. However, its beneficial property cannot be utilized when missing values are present, which should not be simply ignored when estimating the spectral density matrix in the DPCA procedure. Based on a novel combination of conventional DPCA and self-consistency concept, we propose a DPCA method when missing values are present. We demonstrate the advantage of the proposed method over some existing imputation methods through the Monte Carlo experiments and real data analysis.     

面板数据的有序聚类分析及其应用——以全球气候变化聚类分析为例

面板数据的有序聚类分析是多元统计分析的新兴研究领域。借鉴多元统计学中主成分分析方法对面板数据在时间变量上进行降维处理,把变异信息的损失降低到最小,较为准确地反映了样本在各时间段内的整体变化水平;采用费希尔最优求解算法对主成分得分进行有序聚类,为研究有序面板数据的亲疏关系提供一些思路;对全球气候变化进行聚类分析,分析五十年来全球及区域气候变化特点,与国外研究结论对比,显示出良好的应用性。