一种改进的散点图矩阵及其在R软件中的实现

文章讨论了两种扩展的散点图:三维散点图和散点图矩阵,分析了散点图矩阵存在的问题,针对散点图矩阵存在的问题提出了改进的方法,给出了改进的散点图在R软件中的实现方法.     

偏最小二乘回归在SPSS软件中的实现

偏最小二乘回归是第二代回归分析方法,目前已在各种领域得到广泛应用.文章通过详细介绍不同版本的SPSS软件中PLS模块的安装来说明偏最小二乘回归方法在SPSS软件中的实现,并结合实例进一步说明该方法的参数设置和结果的解释.实例分析表明:偏最小二乘回归能够解决变量间多重共线性问题,适合在样本数小于变量个数情形下对系统进行回归建模.     

语言混合加权平均距离测度及其在决策中的应用

对语言加权距离测度进行了进一步研究,提出一种既考虑变量权重又考虑序权重的语言混合加权平均距离测度,分析了该距离测度的优良性质。据此针对属性权重为实数,属性取值为语言术语的多属性决策问题,提出一种基于语言距离的多属性决策方法,最后,通过算例分析说明该方法的可行性和有效性。     

多图模型及其在宏观经济指标相关分析中的应用

多图模型表示来自于不同类的同一组随机变量间的相关关系,结点表示随机变量,边表示变量之间的直接联系,各类的图模型反映了各自相关结构特征和类间共同的信息。用多图模型联合估计方法,将来自不同个体的数据按其特征分类,假设每类中各变量间的相依结构服从同一个高斯图模型,应用组Lasso方法和图Lasso方法联合估计每类的图模型结构。数值模拟验证了多图模型联合估计方法的有效性。用多图模型和联合估计方法对中国15个省份13个宏观经济指标进行相依结构分析,结果表明,不同经济发展水平省份的宏观经济变量间存在共同的相关联系,反映了中国现阶段经济发展的特征;每一类的相关结构反映了各类省份经济发展独有的特征。     

Estimation of Several Intraclass Correlation Coefficients

An intraclass correlation coefficient observed in several populations is estimated. The basis is a variance-stabilizing transformation. It is shown that the intraclass correlation coefficient from any elliptical distribution should be transformed in the same way. Four estimators are compared. An estimator where the components in a vector consisting of the transformed intraclass correlation coefficients are estimated separately, an estimator based on a weighted average of these components, a pretest estimator where the equality of the components is tested and then the outcome of the test is used in the estimation procedure, and a James-Stein estimator which shrinks toward the mean.     

Partial Correlation in Terms of Path Coefficients

The distribution of members of the American Statistical Association (ASA) by several demographic and professional measures is characterized. The analysis is based on a 1979 survey of ASA members who resided in the U.S. More detailed analysis focuses on how demographic and professional characteristics affect the distribution of income and the odds of participating in ASA activities. Several interesting observations are made. Years of experience since highest degree is the most important predictor of income. Highest degree and whether employed in academia are also important. There is a significant difference between the distribution of income for men and women; although the difference is insignificant at one year of experience, it increases with the experience level. Although the survey represented a 100% sample of blacks, Hispanics, and native Americans in the ASA, there is insufficient data to formulate a detailed model of income for this minority group; its average income, however, falls below the expected income of the majority population for higher experience levels. For both the odds of attending annual meetings and serving ASA as an officer or committee member, the most important discriminator is the highest degree of the member. Race is also a significant factor: blacks, Hispanics, and native Americans were least likely to attend annual meetings, and Asians and Pacific Islanders were least likely to hold office. Years of experience is important also for predicting the odds of having held office but not of having attended meetings.     

Location and Scale Estimation with Correlation Coefficients

This article shows how to use any correlation coefficient to produce an estimate of location and scale. It is part of a broader system, called a correlation estimation system (CES), that uses correlation coefficients as the starting point for estimations. The method is illustrated using the well-known normal distribution. This article shows that any correlation coefficient can be used to fit a simple linear regression line to bivariate data and then the slope and intercept are estimates of standard deviation and location. Because a robust correlation will produce robust estimates, this CES can be recommended as a tool for everyday data analysis. Simulations indicate that the median with this method using a robust correlation coefficient appears to be nearly as efficient as the mean with good data and much better if there are a few errant data points. Hypothesis testing and confidence intervals are discussed for the scale parameter; both normal and Cauchy distributions are covered.     

Nonparametric Tests for Comparing Several Coefficients of Variation

We consider the problem of comparing (k + 1) coefficients of variation. We are interested in testing the null hypothesis that the coefficients of variation are equal against each of the alternatives: (a) some populations have different coefficients of variation and (b) the coefficients of variation are ordered. Three nonparametric test statistics are proposed and their asymptotic theory is developed. We compared the proposed tests together with another parametric test using two Monte Carlo studies to estimate their probabilities of Type I error and powers. An illustration of the proposed tests using a real data set is given.     

A Small Sample Test for the Equality of Intraclass Correlation Coefficients Under Unequal Family Sizes for Several Populations

The set of all distinct blocks of a BIBD(v,b,r,k,λ) is referred to as the support of the design. In this paper, the family of BIB designs with v=9 and k=3 is studied from the view of possible support sizes, b*'s. A table is constructed of designs with support sizes belonging to {12,18,20,21,…,84}, for minimum possible b in each case and for any larger admissible b. In constructing this table the methods of trade-off and composition of designs are utilized     

Four Correlation Coefficients with a Third Blocking Variable: Their Efficacy,Relative Efficiency,and Test Statistics

Abstract

The efficacy and the asymptotic relative efficiency (ARE) of a weighted sum of Kendall's taus, a weighted sum of Spearman's rhos, a weighted sum of Pearson's r's, and a weighted sum of z-transformation of the Fisher–Yates correlation coefficients, in the presence of a blocking variable, are discussed. The method of selecting the weighting constants that maximize the efficacy of these four correlation coefficients is proposed. The estimate, test statistics and confidence interval of the four correlation coefficients with weights are also developed. To compare the small-sample properties of the four tests, a simulation study is performed. The theoretical and simulated results all prefer the weighted sum of the Pearson correlation coefficients with the optimal weights, as well as the weighted sum of z-transformation of the Fisher–Yates correlation coefficients with the optimal weights.     

Tests on the Equality of Two Multiple Correlation Coefficients

Asymptotic tests are suggested for testing the equality of two multiple correlation coefficients calculated from a single sample from a multivariate normal distribution. An F test is possible only when the two dependent variables coincide and one set of independent variables is a subset of the second set. Tests are compared by simulation for situations in which the F test is inapplicable. Special attention is paid to cases in which asymptotic normality of the test statistics does not hold.     

A Note on the Geometric Representation of the Correlation Coefficients

Four widely used statistical program packages—BMDP, SPSS, DATATEXT, and OSIRIS—were compared for computational accuracy on sample means, standard deviations, and correlations. Only one, BMDP, was not seriously inaccurate in calculations on a data set of three observations. Further, SPSS computed inaccurate statistics in a discriminant analysis on a real data set of 848 observations. It is recommended that the desk calculator algorithm, found in most of these programs, not be used in packages which may run on short word length machines.     

Bayes Estimation of Intraclass Correlation Coefficients Under Unequal Family Sizes

Bayesian inference for the intraclass correlation ρ is considered under unequal family sizes. We obtain the posterior distribution of ρ and then compare the performance of the Bayes estimator (posterior mean of ρ) with that of Srivastava's (1984) estimator through simulation. Simulation study shows that the Bayes estimator performs better than the Srivastava's estimator in terms of lower mean square error. We also obtain large sample posteriors of ρ based on the asymptotic posterior distribution and based on the Laplace approximation.     

投入产出系数作用新探及其实证分析

直接消耗系数是生产单位j总产出要直接消耗的i产品量,反映j产品部门与i产品部门的生产技术联系,是建立投入产出模型的最基本系数;分配系数是i产品部门分配（提供）给各个部门作生产使用和提供给社会最终使用的数量占该部门产品总量的比重。目前对这些系数的作用阐述得不够充分,文章进一步从行、列、行和、列和的角度探讨它们的作用,也探讨其它一些可以直接从投入产出表计算的系数的新作用,并用中国2002年投入产出表系数进行分析。