典型相关分析中的统计检验问题

一、典型相关分析适用性检验 典型相关分析是研究两组变量之间相关关系的一种统计方法,但是并非所有的截面数据都适合于典型相关分析.     

地区高科技企业创新能力的典型相关分析

文章结合中国高科技产业统计年鉴数据,对高科技企业分省域统计数据中的企业创新能力投入变量与创新能力产出变量作典型相关分析,表明第一典型变量对高科技企业创新投入能力与产出能力之间的相关性有足够的解释力,并且高科技企业创新投入能力主要受技术引进投入和企业专利申请率水平影响,企业创新产出能力主要由新产品产值决定。     

稳健典型相关分析及应用

典型相关分析是重要的多元统计分析方法。本文介绍了基于稳健散布阵的稳健典型相关分析方法,并通过实例说明稳健典型相关分析的应用价值。     

基于典型相关分析的青少年自我中心与攻击行为关系研究

探究青少年自我中心与攻击行为的作用机制,能够为预防青少年犯罪提供参考。采用整群抽样的方法,选取山东省某中学586名学生,以自我中心问卷和攻击行为问卷为研究工具,探究青少年自我中心对攻击行为的影响。结果表明：青少年与父母的关系和自我中心、攻击行为存在显著相关关系（r自=0.209,p自<0.01;r攻=0.249,p攻<0.01）;青少年自我中心与攻击行为之间存在显著正相关（r=0.696,p<0.01）;较高假想观众和个人神话水平伴随较高的敌意。结论：青少年自我中心水平可以正向预测攻击水平,且自我中心水平与敌意水平具有更高相关性。     

企业品牌延伸影响因素的典型相关分析

文章运用典型相关分析方法,通过对问卷调查结果的定量分析,发现了消费者因素、母品牌因素和营销环境因素对企业品牌延伸有重要影响作用,且不同的因素在影响企业品牌延伸程度上存在显著差异。在企业品牌延伸的过程中,充分利用这些影响因素,可避免资金、人力等方面的浪费,提高品牌延伸的成功率,达到稳步提高本企业核心竞争力的目的。     

我国农业经济发展影响因素的实证研究——基于典型相关模型的计量分析

我国是一个农业大国,农业是整个国民经济的基础产业,农业是否能够稳定发展关系到整个国民经济能否健康发展。本文采用典型相关分析方法,构建农业经济发展及其影响因素的综合指标体系,借助SAS软件,对家庭承包责任制在全国范围普遍施行后农业经济增长因素加以实证研究,分析各影响因素对农业经济增长的影响大小和特征,并在此基础上,对我国的农业经济发展战略提出政策建议。     

基于典型相关分析的3E系统协调度评价研究

"十二五"时期既是中国实现工业化的关键时期,也是转变经济结构、提高城市化水平、优化居民消费结构、改善环境与公众健康的重要阶段,这都需要以能源-经济-环境(3E)系统协调发展为保证。因此,在典型相关分析的基础上建立3E系统协调度评价模型,并利用其对中国29个省市区的3E系统协调度进行综合评价,实证结果表明:河北、广东等13个省市区处于中度失调状态;北京、上海等16个省市区呈轻度失调状态。     

中国寿险业效率测算的指标体系研究:基于典型相关分析方法

投入产出指标体系是测算效率的基础,但目前保险业在这点上并没有统一的理论标准和具体体系。与以往学者从理论上进行筛选的方法不同,本文在已有文献的研究基础上,基于2006-2010年中国寿险业32家公司的面板数据,采用典型相关分析方法研究投入和产出指标间的关系,发现流动资产、固定资产、营业费用、佣金支出与赔款支出、保费收入、投资收益分别在反映投入和产出水平方面占主导地位,长期投资、其他投资和准备金增加值是抑制变量。     

典型相关分析与Fisher判别法关系探讨

文章从典型相关分析的原理及相关结论出发,探讨了典型相关分析与多元线性回归分析之间的关系,并利用其相关结论导出了典型相关分析与Fisher判别法的种种关系,最后以一实例分别借助SPSS与SAS输出结果对其关系给予了印证说明.     

论经济变量相关分析的统计方法

在现实经济生活中,经济变量间的相关关系是大量存在的。如投入与产出、收入与支出、生产与消费、投资与经济增长等经济变量都是相互关联的。对这类经济变量间相互依存关系的分析就属于相关分析的内容。在对经济变量间的关系作相关分析时,不仅要根据经济理论和经济含义去定性认识,更重要的是要运用数理统计方法对它们的相关程度作定量测定。     

Canonical Correlation Analysis Through Linear Modeling

In this paper, we introduce linear modeling of canonical correlation analysis, which estimates canonical direction matrices by minimising a quadratic objective function. The linear modeling results in a class of estimators of canonical direction matrices, and an optimal class is derived in the sense described herein. The optimal class guarantees several of the following desirable advantages: first, its estimates of canonical direction matrices are asymptotically efficient; second, its test statistic for determining the number of canonical covariates always has a chi‐squared distribution asymptotically; third, it is straight forward to construct tests for variable selection. The standard canonical correlation analysis and other existing methods turn out to be suboptimal members of the class. Finally, we study the role of canonical variates as a means of dimension reduction for predictors and responses in multivariate regression. Numerical studies and data analysis are presented.     

广东省第三产业经济与旅游经济的典型相关对比分析

改革开放以来，广东经济得到了前所未有的发展，第三产业经济和旅游经济迅猛壮大。第三产业的蓬勃发展，为旅游经济提供了坚实的物质基础；反过来，广东省各地在发展旅游业的同时又与当地经济相结合，带动了当地经济腾飞，促进了广东经济的发展。通过对1998年和2003年广东省各地区第三产业经济和旅游经济的典型相关对比分析，揭示了第三产业经济和旅游经济二者的典型相关关系变化，为制定相应政策提供依据。     

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.     

Canonical correlation analysis in the definition of weight restrictions for data envelopment analysis

This work investigates the use of canonical correlation analysis (CCA) in the definition of weight restrictions for data envelopment analysis (DEA). With this purpose, CCA limits are introduced into Wong and Beasley's DEA model. An application of the method is made over data from hospitals in 27 Brazilian cities, producing as outputs average payment (average admission values) and percentage of hospital admissions according to disease groups (International Classification of Diseases, 9th Edition), and having as inputs mortality rates and average stay (length of stay after admission (days)). In this application, performance scores were calculated for both the (CCA) restricted and unrestricted DEA models. It can be concluded that the use of CCA-based weight limits for DEA models increases the consistency of the estimated DEA scores (more homogenous weights) and that these limits do not present mathematical infeasibility problems while avoiding the need for subjectively restricting weight variation in DEA.     

县域经济与城市化的相关分析

县域经济是指在县域行政区间或其经济空间范围内的经济,包括县、市(县级)、区经济。2004年县域经济在全国经济总量中占55.15%,人口占全国总人口的70.9%,在我国国民经济中占有举足轻重的地位。我国有70%以上的人口生活在县域,可见,县域的城市化是实现中国城市化的基础与关键所在     

Extremes of Determinants and Optimality of Canonical Variables

Extremes of quadratic forms have been presented by several authors (Okamoto, 1969; Rao, 1973; Seber, 1984). The obvious multivariate extension of the extreme of quadratic forms is the extreme of the determinants as well as the ratios of the determinants. In this paper we develop some supremums of the determinants and the ratios of the determinants. A new optimality and equations of canonical variables are obtained.     

Canonical Correlation Analysis Using Small Number of Samples

Canonical correlation assesses the relationship between two groups of variables. Although it has been a useful tool in a wide variety of research areas, it is not well known that weaker canonical correlations require larger sample sizes to be correctly inferred. In this article, we investigate small sample bias in canonical correlation analysis and apply the jackknife bias correction to the estimation of canonical correlations. We use bootstrap samples to obtain a better confidence interval for the jackknife canonical correlation estimator.     

High-dimensional Canonical Forest

Recently, a new ensemble classification method named Canonical Forest (CF) has been proposed by Chen et al. [Canonical forest. Comput Stat. 2014;29:849–867]. CF has been proven to give consistently good results in many data sets and comparable to other widely used classification ensemble methods. However, CF requires an adopting feature reduction method before classifying high-dimensional data. Here, we extend CF to a high-dimensional classifier by incorporating a random feature subspace algorithm [Ho TK. The random subspace method for constructing decision forests. IEEE Trans Pattern Anal Mach Intell. 1998;20:832–844]. This extended algorithm is called HDCF (high-dimensional CF) as it is specifically designed for high-dimensional data. We conducted an experiment using three data sets – gene imprinting, oestrogen, and leukaemia – to compare the performance of HDCF with several popular and successful classification methods on high-dimensional data sets, including Random Forest [Breiman L. Random forest. Mach Learn. 2001;45:5–32], CERP [Ahn H, et al. Classification by ensembles from random partitions of high-dimensional data. Comput Stat Data Anal. 2007;51:6166–6179], and support vector machines [Vapnik V. The nature of statistical learning theory. New York: Springer; 1995]. Besides the classification accuracy, we also investigated the balance between sensitivity and specificity for all these four classification methods.     

An empirical comparison of Canonical Correspondence Analysis and STATICO in the identification of spatio-temporal ecological relationships

The wide-ranging and rapidly evolving nature of ecological studies mean that it is not possible to cover all existing and emerging techniques for analyzing multivariate data. However, two important methods enticed many followers: the Canonical Correspondence Analysis (CCA) and the STATICO analysis. Despite the particular characteristics of each, they have similarities and differences, which when analyzed properly, can, together, provide important complementary results to those that are usually exploited by researchers. If on one hand, the use of CCA is completely generalized and implemented, solving many problems formulated by ecologists, on the other hand, this method has some weaknesses mainly caused by the imposition of the number of variables that is required to be applied (much higher in comparison with samples). Also, the STATICO method has no such restrictions, but requires that the number of variables (species or environment) is the same in each time or space. Yet, the STATICO method presents information that can be more detailed since it allows visualizing the variability within groups (either in time or space). In this study, the data needed for implementing these methods are sketched, as well as the comparison is made showing the advantages and disadvantages of each method. The treated ecological data are a sequence of pairs of ecological tables, where species abundances and environmental variables are measured at different, specified locations, over the course of time.