基于稳健主成分回归的统计数据可靠性评估方法

 稳健主成分回归（RPCR）是稳健主成分分析和稳健回归分析结合使用的一种方法,本文首次运用稳健的RPCR及异常值诊断方法,对2008年我国地区经济增长横截面数据可靠性做了评估。评估结果表明：稳健的RPCR方法能更好的克服异常值的影响,使估计结果更加可靠,并能有效的克服经典的主成分回归（CPCR）方法容易出现的多个异常点的掩盖现象;基本可以认为2008年地区经济增长与相关指标数据是匹配的,但部分地区的经济增长数据可能存在可靠性问题。     

稳健主成分分析在区域技术创新生态系统绩效评价中的应用

鉴于区域技术创新数据中存在指标多而且数据常出现"离群点"的现状,利用稳健主成分方法对于区域技术创新绩效数据进行分析,该方法拚弃了传统方法中均值和方差易受离群点影响的缺点,使得众多区域指标的综合评价更为准确,更能反映客观现实.     

基于SPSS的二次开发直接求解主成分

SPSS是“社会科学统计软件包”(Statistical Package forthe Social Science)的简称,是一种集成化的计算机数据处理应用软件,其简单易懂的菜单式操作方法赢得了大量用户。主成分分析是一种采取数学降维的方法,把多个变量化为少数几个综合变量且互不相关的多元统计分析方法,在实际工作中有着广泛的应用。但是,SPSS软件中没有设置独立的主成分分析模块。要进行主成分分析,则需要借助SPSS中因子分析的输出结果中的因子载荷矩阵,再通过一定的计算,来间接获得主成分分析的结果。这样,一方面用时长,不方便;另一方面由于使用者对SPSS中因子…     

主成分分析法在综合评价经济效益中的误用

主成分分析方法是一种多元统计分析方法,它可以简化数据结构,综合数据信息,因而得到广泛的应用。但主成分分析法应用的必要前提是各变量之间不能相互独立,如果原变量之间相互独立,主成分就是原变量本身,应用这种分析方法就没有意义。     

对多指标综合评价的主成分分析方法的改进

对多指标综合评价的主成分分析方法的改进陈述云,张崇甫国内关于应用主成分分析方法进行综合评价的案例很多。但在众多的案例研究中我们发现,主成分分析的应用还存在一些问题。问题之一：究竟应选取多少个主成分来对样本进行综合评优排序;问题之二：对主成分的经济含义...     

主成分聚类分析有效性的思考

 本文针对经典聚类分析和普通主成分聚类分析极端情形下的失效问题展开讨论,通过定义客观赋权的主成分距离为分类统计量,并以实证检验取得良好效果为依据,有效地解决了主成分聚类分析在极端情形下所不能揭示的问题。     

基于稳健稀疏主成分的经济增长影响因素分析

从传统生产要素、制度、金融和经济结构等四个方面选取了19个影响中国经济增长的变量,运用稳健稀疏主成分方法进行实证分析。结果表明物质资本、城镇化率、金融深度、城镇居民消费结构、基尼系数、技术水平已成为促进中国经济增长的主要动力,但东、中、西部经济增长的主要影响因素互不相同。在此基础上就如何进一步促进中国经济增长和区域经济均衡发展提出了若干政策建议。     

如何正确应用SPSS软件做主成分分析

 鉴于目前很多用SPSS软件分析主成分的教材中和发表的文章中有不少错误之处。本文从主成分分析与因子分析的关系出发,借用SPSS软件自带的数据,进行了正确的操作,并将其结果与SAS软件的结果进行比较,两者完全相同。     

主成分的相关结构

主成分分析作为多元统计分析的方法之一,在许多领域得到了广泛的应用,最近几年在社会经济领域的应用也越来越多,例如综合评价企业的经济效益。评价技术进步经济效益等等。这些应用成果得到了充分的肯定,但也引起不少争议,除了极少数人对主成     

非负约束主成分分析

非负约束主成分分析李平玉一、问题的提出设ＸＰＸ１是Ｐ个指标,在许多实际问题中,要对Ｘ进行加权求一个综合指标Ｙ＝Ａ＇Ｘ,Ａ≥０,Ａ＇１＝１,那么怎样合理地选择权向量Ａ呢？假定Ｅ（Ｘ）＝０,已知Ｖ（Ｘ）＝ＶＰ＝（ＶＩＪ）＝（ΡＩＪΣＩΣＪ）＞０,其中Ｖ是...     

Robust Principal Component Functional Logistic Regression

In this article, we discuss the estimation of the parameter function for a functional logistic regression model in the presence of outliers. We consider ways that allow for the parameter estimator to be resistant to outliers, in addition to minimizing multicollinearity and reducing the high dimensionality, which is inherent with functional data. To achieve this, the functional covariates and functional parameter of the model are approximated in a finite-dimensional space generated by an appropriate basis. This approach reduces the functional model to a standard multiple logistic model with highly collinear covariates and potential high-dimensionality issues. The proposed estimator tackles these issues and also minimizes the effect of functional outliers. Results from a simulation study and a real world example are also presented to illustrate the performance of the proposed estimator.     

稳健因子分析方法的构建及比较研究

由于传统因子分析方法对离群值较敏感,导致计算结果与实际不相符。针对这一现象,本文运用FAST-MCD方法对传统因子分析方法进行改进,构建出因子分析的稳健算法,以克服离群值的影响,并对此方法进行了模拟和实证分析。模拟和实证分析结果均表明：因子旋转前后,当数据中不存在离群值时,传统因子分析与稳健因子分析得到的结果基本保持一致;当数据中存在离群值时,运用传统因子分析得到的结果出现较大变化,而运用稳健因子分析方法得到的结果基本不变,这说明相对于传统因子分析方法,稳健因子分析方法能有效抵抗离群值的影响,具有良好的抗干扰性和高抗差性。     

Comparative Study of Robust Estimators Based on a Sensitivity Coefficient in Principal Component Analysis

This work is devoted to robust principal component analysis (PCA). We give a comparison between some multivariate estimators of location and scatter by computing the influence functions of the sensitivity coefficient ρ corresponding to these estimators, and the mean squared error (MSE) of estimators of ρ. The coefficient ρ measures the closeness between the subspaces spanned by the initial eigenvectors and their corresponding version derived from an infinitesimal perturbation of the data distribution.     

基于稳健MM估计的统计数据质量评估方法

 政府统计数据质量是当前各界关注的热点问题,如何采用严谨的诊断方法,对我国统计数据进行科学的评估具有重要的现实意义。稳健回归方法可使求出的回归估计不受异常值的强烈影响,并且能更好的识别异常点。本文首次运用基于稳健MM估计的异常值诊断方法,在生产函数模型的框架下,分别使用两种不同的劳动投入数据,对改革以来我国GDP数据质量进行了评估。结果表明,基于稳健MM估计的异常值诊断方法可有效的解决传统方法容易出现的多个异常点的掩盖现象,改革以来我国的GDP数据是相对可靠的。     

Robust estimates for GARCH models

In this paper we present two robust estimates for GARCH models. The first is defined by the minimization of a conveniently modified likelihood and the second is similarly defined, but includes an additional mechanism for restricting the propagation of the effect of one outlier on the next estimated conditional variances. We study the asymptotic properties of our estimates proving consistency and asymptotic normality. A Monte Carlo study shows that the proposed estimates compare favorably with respect to other robust estimates. Moreover, we consider some real examples with financial data that illustrate the behavior of these estimates.     

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.     

Robust Liu-type estimator for regression based on M-estimator

The problem of multicollinearity and outliers in the dataset can strongly distort ordinary least-square estimates and lead to unreliable results. We propose a new Robust Liu-type M-estimator to cope with this combined problem of multicollinearity and outliers in the y-direction. Our new estimator has advantages over two-parameter Liu-type estimator, Ridge-type M-estimator, and M-estimator. Furthermore, we give a numerical example and a simulation study to illustrate some of the theoretical results.     

Sparse Principal Component Analysis in Hilbert Space

Technical advances in many areas have produced more complicated high‐dimensional data sets than the usual high‐dimensional data matrix, such as the fMRI data collected in a period for independent trials, or expression levels of genes measured in different tissues. Multiple measurements exist for each variable in each sample unit of these data. Regarding the multiple measurements as an element in a Hilbert space, we propose Principal Component Analysis (PCA) in Hilbert space. The principal components (PCs) thus defined carry information about not only the patterns of variations in individual variables but also the relationships between variables. To extract the features with greatest contributions to the explained variations in PCs for high‐dimensional data, we also propose sparse PCA in Hilbert space by imposing a generalized elastic‐net constraint. Efficient algorithms to solve the optimization problems in our methods are provided. We also propose a criterion for selecting the tuning parameter.     

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.