半偏相关系数及其在经济增长贡献测算中的应用

一、关于半偏相关系数的涵义在多元回归分析中遇到的问题之一就是确定每个解释变量对复相关系数的贡献,我们曾经用到过的解决办法是计算简单相关系数和偏相关系数。简单相关系数是衡量两个变量之间相关性程度的相关系数,反映的是两个变量之间局部的相关关系;偏相关系数是在多元     

浅议相关系数与偏相关系数的使用

相关分析是经济统计学的重要内容之一。在相关分析中,人们通常利用两个经济变量之间的简单相关系数(即相关系数)和一个经济变量与多个经济变量之间的复相关系数来分析和测定这些经济变量之间的线性相关程度,并据此进行线性回归分析、预测和控制等。 我们知道,相关系数是刻划变量之间线性相关     

偏典型相关系数及其应用

一、偏典型相关系数的概念 我们知道,偏相关系数是在p+1个变量Y,X_1,X_2,…X_p中固定其他变量,而研究其中的任意两个变量的相关方向与程度的统计指标。偏相关系数在多变量分析中,与简单相关系数相比较,由于它考虑周围变量的变动及对所研究变量的不同影响,并且进行控制,克服了简单相关系数的不足,能真实反映两变量之间的本质的相关方向与程度。     

我国距离现代化的目标还有多远?

我国距离现代化的目标还有多远？李强，张志英改革开放以来。我国人民的生活水平和国家的经济实力都有了很大的提高。那么，时至今日，我国究竟达到什么样的发展水产了呢？我们距离现代化的发展目标究竟还有多远呢？关于现代化的发展水平，国际上有不同的测量指标，比较常...     

厉明同志为什么不愿作统计工作?

我们收到厉明同志的一封信,信中反映了他对统计工作的一些看法和在工作中的苦闷情绪,我们认为这个思想认识问题目前在我们不少统计干部中是或多或少存在的,因此现在把这封信发表出来,供大家讨论,这对大家是会有益处的.根据厉明同志的来信,现提出以下三个问题,希望大家围绕这些问题热烈发表意见:(一)厉明同志认为统计工作只不过是一些加加减减算算百分比的工作,枯燥无味,这样的认识对不对?我们应该怎样正确地认识统计工作?(二)厉明同志认为做统计工作起不了们什么大的作用?这种看法对不对?为们么?我们应该怎样来认识统计工作在整个国家建设中的地位和作用?又怎样来发挥统计工作的作用?(三)厉明同志对统计工作失去信心,不知道统计工作者的真实前途何在,作统计工作就不能提高自己,那末统计工作者到底有没有前途呢?前途又是什么呢?作统计工作是不是就不能提高自己呢?参加讨论的来稿内容要具体,最好集中一个问题结合自己的亲身体会,联系具体事例来分析和说明道理,不要泛泛发表空洞的议论.来稿请自留底稿,我们不准备退还.     

挥挥手,你丢失的不仅仅是青春

【正】人这一辈子,在身上挥之不去的,除了失败,我想就是烦恼了。你现在在烦恼什么呢?是烦恼学业上的不足,还是工作上的不顺,还是爱情的痛苦,还是生病的无耐?其实,烦恼有些时候是我们自己创造出来的,烦恼它不会凭空的出现,烦恼总是在我们思想中繁衍生息,有的时候静下心来,想想烦恼又算什么呢?每个人都只有24小时,如果被烦恼占据了...     

基于因子分析的医院临床学科综合实力评价

为了全面、客观地评价医院各临床学科综合管理能力和水平,从而改进并推动各临床学科的进一步发展,往往要综合考虑众多管理指标即变量。多变量无疑为科学研究和评价提供了大量的信息,但在一定程度上也增加了分析问题的难度。所以可以利用因子分析法,根据相关性大小把变量分组,使得同组内变量之间相关性较高、不同变量之间相关性较低,每组变量代表一个基本结     

多主题抽样调查中改进估计方法的研究

多主题抽样调查在实际统计工作中非常普遍,即一项调查同时涉及两个或多个目标变量(指标),对总体的推算也需要同时对这两个或多个指标进行估计.通常同一调查中的多个目标变量之间会具有相关性,利用这一信息可以提高对所关注调查指标的估计精度.本文利用多重多元线性模型的方法研究这一问题,讨论了最佳线性模型无偏估计和一般回归估计,可以看到借助调查指标之间的相关性,较之常用的单个响应变量的多元线性回归模型方法,得到的最佳线性模型无偏估计和一般回归估计都可以有效地提高对总体总量的估计精度,本文的数值模拟和实例分析也验证了这一结论.     

几种选取部分代表性指标的统计方法

在统计工作中,经常遇到从总体中选取一部分有代表性的指标反映总体的问题。解决这一问题有两个途径:一是从指标体系去分析这些指标之间的关系,找出一部分代表性强的指标;另一种从数据出发,用数理统计的方法选取一部分“代表”性指标(即变量)。本文要谈的就是后一种方法,当然,最好是能把这两种方法结合起来,怎样去结合,有待于进一步的研究。     

金融风险统计度量标准研究

一、问题的提出及意义1 999年 ,Artzner,etal公开发表了他们的研究“一致性风险度量” ,推动了风险度量问题的研究[1 ] 。从风险度量的发展过程 ,有很多种风险度量被提出 ,各自都在阐述自己方法的优点 ,可以说风险度量论坛众说纷纭。用什么来度量金融风险的大小 ?究竟如何正确理解风险 ?应该如何去合理的度量 ?选用什么样的风险指标 ?风险度量有没有一个统一的标准框架 ?在标准框架下各种风险度量有何不同 ?有没有新的度量方法 ?金融风险度量标准追根求源的研究和讨论越来越受到学术界关注。　　二、风险特征及其度量公理人们基于不同的目…     

On multivariate Gaussian copulas

Gaussian copulas are handy tool in many applications. However, when dimension of data is large, there are too many parameters to estimate. Use of special variance structure can facilitate the task. In many cases, especially when different data types are used, Pearson correlation is not a suitable measure of dependence. We study the properties of Kendall and Spearman correlation coefficients—which have better properties and are invariant under monotone transformations—used at the place of Pearson coefficients. Spearman correlation coefficient appears to be more suitable for use in such complex applications.     

Asymptotic variances of maximum likelihood estimator for the correlation coefficient from a BVN distribution with one variable subject to censoring

This paper deals with the problem of estimating the Pearson correlation coefficient when one variable is subject to left or right censoring. In parallel to the classical results on the Pearson correlation coefficient, we derive a workable formula, through tedious computation and intensive simplification, of the asymptotic variances of the maximum likelihood estimators in two cases: (1) known means and variances and (2) unknown means and variances. We illustrate the usefulness of the asymptotic results in experimental designs.     

Some New Results on the Multinomial Randomized Response Model

ABSTRACT

The randomized response technique is an effective survey method designed to elicit sensitive information while ensuring the privacy of the respondents. In this article, we present some new results on the randomization response model in situations wherein one or two response variables are assumed to follow a multinomial distribution. For a single sensitive question, we use the well-known Hopkins randomization device to derive estimates, both under the assumption of truthful and untruthful responses, and present a technique for making pairwise comparisons. When there are two sensitive questions of interest, we derive a Pearson product moment correlation estimator based on the multinomial model assumption. This estimator may be used to quantify the linear relationship between two variables when multinomial response data are observed according to a randomized-response protocol.     

Estimating the correlation coefficient in the presence of correlated observations from a bivariate normal population

Estimation of the correlation coefficient between two variates (p) in the presence of correlated observations from a bivar iate normal population is considered The estimated maximum likelihood estimator (EMLE), an estimate based on the maximum likelihood estimator (MLE), is proposed and studied for the estimation of p For the large sample case , approximate expressions foi the variance and the bias of the Pearson estimate of the correlation coefficient are derived. These expressions suggests that the Pearson’s estimator possesses high mean square error (MSE) in estimating ρ in comparison to the MLE The MSE is particularly high when the observations within clusters aie highly correlated. The Pearson’s estimate, the MLE, and the EMLE aie evaluated in a simulation study This study shows that the proposed EMLE pefoims bettei than the Pearson’s correlation coefficient except when the number of clusters is small.     

Some Statistical Methods in Assessing Linear Relational Agreement: An Empirical Comparative Study

Although multiple indices were introduced in the area of agreement measurements, the only documented index for linear relational agreement, which is for interval scale data, is the Pearson product-moment correlation coefficient. Despite its meaningfulness, the Pearson product-moment correlation coefficient does not convey the practical information such as what proportion of observations is within a certain boundary of the target value. To address this need, based on the inverse regression, we proposed the adjusted mean squared deviation (AMSD), adjusted coverage probability (ACP), and adjusted total deviation index (ATDI) for the measurement of the relational agreement. They can serve as reasonable and practically meaningful measurements for relational agreement. Real life data are considered to illustrate the performance of the methods.     

Robustness and monotonicity properties of generalized correlation coefficients

A new class of generalized correlation coefficients that contains the Pearson and Kendall statistics as special cases was defined by Chinchilli et al. (2005) and applied to the estimation of correlations coefficients within the context of 2×2 cross-over designs for clinical trials. In this paper, we determine the infinitesimal robustness and local stability properties of these generalized correlation coefficients by deriving their corresponding influence functions. For cases in which the population distribution is a bivariate normal or a mixture of bivariate normal distributions we obtain explicit formulas, and establish monotonicity and sign-reverse rule properties of the generalized correlation coefficients.     

A comparative study for robust canonical correlation methods

The aim of this study is to obtain robust canonical vectors and correlation coefficients based on the percentage bend correlation and winsorized correlation in the correlation matrix and fast consistent high breakdown (FCH), reweighted fast consistent high breakdown (RFCH), and reweighted multivariate normal (RMVN) estimators to estimate the covariance matrix and then compare these estimators with the existing estimators. In the correlation matrix of canonical correlation analysis (CCA), we present an approach that substitutes the percentage bend correlation and the winsorized correlation in place of the widely employed the Pearson correlation. Moreover, we employ the FCH, RFCH, and RMVN estimators to estimate the covariance matrix in the CCA. We conduct a simulation study and employ real data with the objective of comparing the performance of the different estimators for canonical vectors and correlation with that of our proposed approaches. The breakdown plots and independent tests are employed as differentiating criteria of the robustness and performance of the estimators. Based on our computational and real data studies, we propose suggestions and guidelines on the practical implications of our findings.     

A linear model-based test for the heterogeneity of conditional correlations

Current methods of testing the equality of conditional correlations of bivariate data on a third variable of interest (covariate) are limited due to discretizing of the covariate when it is continuous. In this study, we propose a linear model approach for estimation and hypothesis testing of the Pearson correlation coefficient, where the correlation itself can be modeled as a function of continuous covariates. The restricted maximum likelihood method is applied for parameter estimation, and the corrected likelihood ratio test is performed for hypothesis testing. This approach allows for flexible and robust inference and prediction of the conditional correlations based on the linear model. Simulation studies show that the proposed method is statistically more powerful and more flexible in accommodating complex covariate patterns than the existing methods. In addition, we illustrate the approach by analyzing the correlation between the physical component summary and the mental component summary of the MOS SF-36 form across a fair number of covariates in the national survey data.     

Testing equality of correlation coefficients in two populations via permutation methods

The present paper investigates the asymptotic behaviour of a studentized permutation test for testing equality of (Pearson) correlation coefficients in two populations. It is shown that this test is asymptotically of exact level and has the same power for contiguous alternatives as the corresponding asymptotic test. As a by-product we specify the assumptions needed for the validity of the permutation test suggested in Sakaori (2002). A small simulation study compares the finite sample properties of the considered tests.     

An approximation to the distribution of the product of two dependent correlation coefficients

Many methodological studies depend on the product of two dependent correlation coefficients. However, the behavior of the distribution of the product of two dependent correlation coefficients is not well known. The distribution of sets of correlation coefficients has been well studied, but not the distribution of the product of two dependent correlation coefficients. The present study derives an approximation to the distribution of the product of two dependent correlation coefficients with a closed form, resulting in a Pearson Type I distribution. A simulation study is also conducted to assess the accuracy of the approximation.