主成分分析法在企业评价中的应用

主成分分析法是将分散在一组变量上的众多信息集中到少数几个综合指标(主成分)上,以便于描述数据集内部结构,在社会、经济研究中有着十分广泛的应用。目前许多工作者采用此方法建立综合评价函数,对企业的经济效益、技术经济水平进行综合评价。     

基于改进的主成分分析法的县域竞争力综合评价研究

文章针对传统主成分分析法在复杂系统高维指标评价中的局限性,首先建立了改进主成分分析模型,然后基于改进的模型构建了县域竞争力评价指标体系,最后,给出了该评价系统在我国不同县域竞争力综合评价中的应用实例.结果表明:该研究方法在我国县域竞争力分析评价中具有积极的现实意义.     

基于复杂系统综合评价的二重主成分分析法

在分析主成分分析在权系数、降维效果等问题的基础上,提出了对复杂系统的综合评价首先要对指标体系分类的各个方面进行主成分分析,在得到各自方面的评价值后再进行主成分分析,最终得到综合评价值的二重主成分分析法.最后从理论和以上市公司经营业绩评价为例检验了这种方法的有效性.     

主成分综合评价方法存在的问题及改进

文章深入分析了用目前普遍采用的主成分分析法进行多指标综合评价时存在的指标权系数不合理问题,并对用主成分构建综合评价函数的方式作了改进,使综合评价函数的权系数变得较为合理。     

人力资本水平的综合评价研究——主成分分析法

基于现有人力资本水平测度方法的不足,本文从人力资本的定义出发,构建人力资本水平测度指标体系,并在此体系的基础上利用主成分分析法对我国各地区的人力资本水平进行评价,得出我国地区人力资本分布不均的结论。     

主成分分析法在钢铁行业上市公司业绩评价中的应用

钢铁行业是我国的传统行业,其上市公司大多具有国有背景。近年来,随着国企改革力度的加大,其日益成为市场关注的焦点。特别是入世后,钢铁行业将面临国外竞争对手的强大挑战,因此,对于我国钢铁行业上市公司的综合实力有一个全面的认识,对于广大投资者来说,具有十分重要的现实意义。文章运用主成分分析方法,对我国钢铁行业上市公司的经营业绩进行了综合评价,并进行了相关分析。     

主成分分析与VARCLUS在综合评价中的异同比较

主成分分析和VARCLUS是两种较重要的多元统计分析方法,二者既存在一定的联系,又有着明显的区别.文章从方法、概念、基本思想、教学模型、综合指标数目的判断方法、计算过程诸方面,较详尽地探讨二者的异同,并举例说明二者在实际问题中的应用.     

主成分分析综合评价应该注意的问题

将主成分分析用于多指标的综合评价较普遍,但因缺乏应用条件的考虑而导致评价结果不具合理性甚至错误,故应深入研究其应用条件.本文应用因子分析法因子载荷阵的简单结构、加权算术平均数的合理性,得出主成分分析综合评价的应用条件是:指标是正向、标准化的,主成分载荷阵达到更好的简单结构,主成分正向,主成分与变量显著相关;并结合2010年广东省各市对外贸易国际竞争力的评价实例提出了一些建议.     

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.     

主成分分析法在财务预警实证研究中的应用

文章以西安电力集团公司为研究样本,通过对我国企业财务危机状况的实证研究,建立了企业财务预警模型。特别是采用统计方法中的主成分分析法,来确定影响因素中若干指标的权重,可避免人为赋值的弊端,客观的揭示企业在经营方面的问题。     

The Impact of Measurement Error on Principal Component Analysis

We investigate the effect of measurement error on principal component analysis in the high‐dimensional setting. The effects of random, additive errors are characterized by the expectation and variance of the changes in the eigenvalues and eigenvectors. The results show that the impact of uncorrelated measurement error on the principal component scores is mainly in terms of increased variability and not bias. In practice, the error‐induced increase in variability is small compared with the original variability for the components corresponding to the largest eigenvalues. This suggests that the impact will be negligible when these component scores are used in classification and regression or for visualizing data. However, the measurement error will contribute to a large variability in component loadings, relative to the loading values, such that interpretation based on the loadings can be difficult. The results are illustrated by simulating additive Gaussian measurement error in microarray expression data from cancer tumours and control tissues.     

基于非线性主成分和聚类分析的综合评价方法

针对传统主成分在处理非线性问题上的不足,阐述了传统方法在数据无量纲化中“中心标准化”的缺点和处理“线性”数据时的缺陷,给出了数据无量纲化和处理“非线性”数据时的改进方法,并建立了一种基于“对数中心化”的非线性主成分分析和聚类分析的新的综合评价方法。实验表明,该方法能有效地处理非线性数据。     

主成分分析与因子分析的异同比较及应用

主成分分析法和因子分析法都是从变量的方差-协方差结构入手,在尽可能多地保留原始信息的基础上,用少数新变量来解释原始变量的多元统计分析方法。教学实践中,发现学生运用主成分分析法和因子分析法处理降维问题的认识不够清楚,本文针对性地从主成分分析法、因子分析法的基本思想、使用方法及统计量的分析等多角度进行比较,并辅以实例。     

大系统的多重主成分评价及其应用

大系统综合评价是综合评价的重要内容之一。文章在分析传统的主成分分析在降维效果、权系数等问题的基础上,提出了一种针对大系统综合评价的改进的主成分评价方法———多重主成分评价。在理论分析其合理性的基础上,最后利用商业银行经营绩效的实例验证了这种方法的有效性。     

A Variable Selection Criterion for Two Sets of Principal Component Scores in Principal Canonical Correlation Analysis

Canonical correlation analysis (CCA) is often used to analyze the correlation between two random vectors. However, sometimes interpretation of CCA results may be hard. In an attempt to address these difficulties, principal canonical correlation analysis (PCCA) was proposed. PCCA is CCA between two sets of principal component (PC) scores. We consider the problem of selecting useful PC scores in CCA. A variable selection criterion for one set of PC scores has been proposed by Ogura (2010), here, we propose a variable selection criterion for two sets of PC scores in PCCA. Furthermore, we demonstrate the effectiveness of this criterion.     

Principal Volatility Component Analysis

Many empirical time series such as asset returns and traffic data exhibit the characteristic of time-varying conditional covariances, known as volatility or conditional heteroscedasticity. Modeling multivariate volatility, however, encounters several difficulties, including the curse of dimensionality. Dimension reduction can be useful and is often necessary. The goal of this article is to extend the idea of principal component analysis to principal volatility component (PVC) analysis. We define a cumulative generalized kurtosis matrix to summarize the volatility dependence of multivariate time series. Spectral analysis of this generalized kurtosis matrix is used to define PVCs. We consider a sample estimate of the generalized kurtosis matrix and propose test statistics for detecting linear combinations that do not have conditional heteroscedasticity. For application, we applied the proposed analysis to weekly log returns of seven exchange rates against U.S. dollar from 2000 to 2011 and found a linear combination among the exchange rates that has no conditional heteroscedasticity.     

多指标综合评价中主成分分析和因子分析方法的比较

文章通过对主成分分析和因子分析在研究目的、分析原理、SPSS软件实现过程方面的比较,指出在多指标综合评价时应用两种方法应该注意四个问题,以正确地进行实证研究。     

Probabilistic Principal Component Analysis

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based on a probability model. We demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model that is closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss, with illustrative examples, the advantages conveyed by this probabilistic approach to PCA.     

主成分与因子分析中指标同趋势化方法探讨

样本主成分和样本因子分析法已成为一种最主要的综合评价方法之一,指标变量的同趋势化是运用该方法的重要步骤。文章总结了主成分与因子分析中指标同趋势化的具体方法,论述了这些方法对综合评价的影响,并指出了这些方法的适用条件。     

Sensitivity Coefficient in Principal Component Analysis: Robust Case

In the classical principal component analysis (PCA), the empirical influence function for the sensitivity coefficient ρ is used to detect influential observations on the subspace spanned by the dominants principal components. In this article, we derive the influence function of ρ in the case where the reweighted minimum covariance determinant (MCD¹) is used as estimator of multivariate location and scatter. Our aim is to confirm the reliability in terms of robustness of the MCD¹ via the approach based on the influence function of the sensitivity coefficient.