属性数据的多变量对应分析模型及应用

属性数据的建模和分析是市场研究活动中最重要的一类应用问题,学术界和市场研究行业一般使用列联表及统计检验的方法进行分析。故将法国统计学家J.P.Beozecri提出的对应分析法导入市场研究实证过程,使问卷调查中常见的多变量属性数据分析建模过程呈现出稳健的统计结论和直观的二维图示,并推广到广义多变量对应分析场合,其结论可靠,有应用创新。     

Q型系统聚类分析中的统计检验问题

Q型系统聚类分析已经越来越成为人们广泛应用的多元统计分析方法。然而在应用中盲目套用系统聚类分析方法的情况很多，并对聚类分析方法的适用性、聚类过程的合理性、聚类结果的有效性等问题分析重视不够，更谈不上对聚类分析进行统计检验。因此，为了更好地应用Q型系统聚类分析，就应对Q型系统聚类分析结果进行统计检验并建立统计检验体系。Q型系统聚类分析统计检验体系主要包括：Q型系统聚类分析结果的有效性检验；聚类分析类（组）数选择合理性检验；聚类变量的显著性检验。     

判别分析统计检验体系的探讨

判别分析已越来越受到人们的重视并取得了重要的应用成果，但应用中存在着简单套用的情况，对判别分析的适用性、判别效果的显著性、判别变量的判别能力以及判别函数的判别能力的检验等问题重视不够。为了更好地应用判别分析，就应对判别分析进行统计检验并建立统计检验体系，统计检验体系应包括：判别分析适用性检验，判别效果显著性检验，判别变量的判别能力检验和判别函数的判别能力检验。     

因子分析统计检验体系的探讨

为了更好地应用因子分析,论文提出建立因子分析统计检验体系,包括因子分析适用性的统计检验以及提取公共因子数目多少的检验,并对如何进行上述检验进行探讨,论文最后还提出了应用因子分析时应注意的其他问题.     

主成分分析中的统计检验问题

主成分分析已经越来越成为人们广泛应用的多元统计分析方法。但应用中盲目套用主成分分析方法的情况很多,而对主成分分析的适用性,主成分个数的合理性等问题重视不够,更谈不上对主成分分析进行统计检验。为此,为了更好应用主成分分析,就应对主成分分析结果进行统计检验并建立统计检验体系。主成分分析统计检验体系主要包括:主成分分析的适用性检验;等相关性检验;主成分方差的假设检验和选取主成分数目检验。     

结构相对数动态变化类型及其统计检验

本文对动态相对数动态变化的类型进行了归纳，提出了相应的统计检验方法，并应用此方法分析我国三次产业演变规律。发现改革开放以来我国三次产业演变有服务化的趋势。     

谱检验的Wild Bootstrap方法

 本文考察了基于谱估计的拟合优度检验在判断时间序列鞅差性质方面的应用，提出了利用Wild Bootstrap来近似该类检验统计量渐近分布的方法，通过模拟试验揭示出新的方法改进了检验的水平并提高了其功效，最后比较了不同方法在分析实际金融数据时的不同效果。     

非参数X^2检验的两个局限性问题

X^2检验在参数检验和非参数检验有着广泛的应用，但在教学和科研中，我们发现X^2检验应用功能被扩大化了，教学和科研人员往往忽略了使用X^2检验的前提条件和应用的局限性。本文着重讨论X^2检验在非参数检验中的两个比较严重的局限性问题，并提出了相应的解决方法．以期提高统计方法应用的准确性．     

方差分析与虚拟变量回归模型的比较研究

方差分析与回归分析分属不同的统计方法,从问题背景到处理手段都有所不同。文章针对单因素方差分析和双因素方差分析,分别找到对应形式的虚拟变量回归模型,通过严格的数学推导,发现两类分析方法的检验原假设等价,检验统计量也等价,并论证了方差分析与回归分析具有内在一致性。     

虚拟变量回归与方差分析的联系

文章从模型本身和检验统计量角度分析发现,虚拟自变量回归线性关系显著性检验与对应的单因素方差分析等价,回归系数的显著性检验与两总体均值的比较关系密切.而行、列因素各为2水平的双因素无重复试验方差分析,也能在回归分析中找到等价的检验.     

A probabilistic model for nonsymmetric correspondence analysis and prediction in contingency tables

Summary Nonsymmetric correspondence analysis is a model meant for the analysis of the dependence in a two-way continengy table, and is an alternative to correspondence analysis. Correspondence analysis is based on the decomposition of Pearson's Ф²-index Nonsymmetric correspondence analysis is based on the decomposition of Goodman-Kruskal's τ-index for predicatablity. In this paper, we approach nonsymmetric correspondence analysis as a statistical model based on a probability distribution. We provide algorithms for the maximum likelihood and the least-squares estimation with linear constraints upon model parameters. The nonsymmetric correspondence analysis model has many properties that can be useful for prediction analysis in contingency tables. Predictability measures are introduced to identify the categories of the response variable that can be best predicted, as well as the categories of the explanatory variable having the highest predictability power. We describe the interpretation of model parameters in two examples. In the end, we discuss the relations of nonsymmetric correspondence analysis with other reduced-rank models.     

A GENEALOGY OF CORRESPONDENCE ANALYSIS

Over the past half a century correspondence analysis has grown from a little known statistical technique designed to graphically depict the association structure of categorical variables that form a contingency table to a very popular tool used in a wide variety of disciplines. Despite this growth, correspondence analysis remains relatively unknown in some parts of the world, including the Australasian statistical community. This paper provides a non‐technical, bibliographic exploration of correspondence analysis. We take a step back to view the development of this statistical technique and provide a brief account of its genealogy with a selection of over 270 key publications that have contributed to its growth. We also look at its maturity over the decades.     

RAO'S SCORE TESTS IN SURVIVAL ANALYSIS: EXAMPLES AND BARTLETT TYPE ADJUSTMENTS

Score method in hypothesis testing is one of Professor C. R. Rao's great contributions to statistics. It provides a simple and unified way to test some simple and composite hypotheses in many statistical problems. Some popular tests in statistical practice derived with the help of intuitions can be shown as score tests under some statistical models. The subject-years test and log-rank test in survival analysis are two of the examples. In this paper, we first introduce these two examples. After formulating these two tests as score tests, we then review some recent results on the Bartlett type adjustments for these tests.     

Investigating the European perception of food using moments obtained from non-symmetrical correspondence analysis

The perception of food in Europe has been a topic of research for many years due to its importance in better understanding the role of food in helping to define the culture of a country. It is also important from a marketing perspective for identifying how consumers relate to food. Recently, this topic was discussed by Guerrero et al. (2010) who used a graphical statistical technique called correspondence analysis to identify the association between the countries that participated in the study and words that were linked with “Traditional” food. This paper explores the use of non-symmetrical correspondence analysis and provides an interpretation of the configuration of points in the graphical display in terms of its first four moments. In particular, we will focus on the skewness and kurtosis of such a configuration. Such measure's provide further detail on the nature of the association between the countries studied and the words linked with “Traditional” food.     

NON-SYMMETRICAL CORRESPONDENCE ANALYSIS WITH CONCATENATION AND LINEAR CONSTRAINTS

Correspondence analysis is a popular statistical technique used to identify graphically the presence, and structure, of association between two or more cross-classified categorical variables. Such a procedure is very useful when it is known that there is a symmetric (two-way) relationship between the variables. When such a relationship is known not to exist, non-symmetrical correspondence analysis is more appropriate as a method of establishing the source of association. This paper highlights some tools that can be used to explore the behaviour of asymmetric categorical variables. These tools consist of confidence regions, the link between non-symmetrical correspondence analysis and the analysis of variance of categorical variables, and the effect of imposing linear constraints. We also explore the application of non-symmetrical correspondence analysis to three-way contingency tables.     

Knowledge acquisition for a supportive user interface for correspondence analysis

We studied the way in which experienced statisticians handle the output of a correspondence analysis program, in order to investigate the possibility of computerized support for the interpretation of complex output from statistical software. Four experts participated in this study, all with experience in consultation and with a high level of theoretical knowledge on the subject. In ‘thinking-aloud sessions' they tried to reach conclusions from two forms of output (first without and then with indication of the meaning of variables). We present results on rule-based reasoning by the experts. Suggestions are given for the application of these results in the construction of an intelligent user interface for correspondence analysis.