虚拟变量在居民消费研究中的应用

一、虚拟变量与回归模型 在现代经济计量分析中,利用模型进行回归分析是应用比较广泛的一种数量分析技术.一般回归分析中变量都是定量变量,这是因为模拟回归需要样本数据.但实际中有时模型仅考虑定量变量是不够的.因为经济现象不仅受一些定量因素的影响,还可能受到一些定性因素的影响.比如不同时期的不同政策,战争、自然灾害等非常时期,人的不同性别、文化程度、婚姻状况等.     

社会调查研究中样本的代表性问题探讨

一、样本的代表性的含义 在一些人的认识中,概率抽样和随机抽样这两个概念似乎存在一定程度上混乱甚至错误,把两者与完全随机抽样等同起来是最极端的表现,所以需要澄清一下."随机现象"指的是一个变量(如居民收入)的取值范围是确定的,但在一次实验(抽样)中到底抽到这个变量的哪个具体值(哪户居民的收入)是不确定的,但在很多次实验之后,变量的取值(平均数、标准差等统计量)又会表现出规律性的现象."概率"指的是一个事物发生的可能性的大小,或者一个变量的各个取值可能被抽到机会的大小.     

关于相关分析与回归分析的比较研究

相关分析与回归分析是统计分析中的基本方法，两者之间既有联系，又有区别。本文拟对这两种分析方法进行一些比较研究。一、相关分析与回归分析的区别研究我们认为，相关分析与回归分析的区别主要表现在如下几点：第一表现为概念上的区别。相关是指一个变量的值与另一个变量的值有连带性。换言之，如果一个变量的值发生变化，另一个变量的值也有变化，则两个变量就相关了。这种相关关系是指变量之间的不确定的依存关系。比如，人的身高和体重，一般地说，身高者体也重，因此身高和体重之间具有相关关系。但是，具有同一身高的人，体重却有差…     

两项相关及其应用

两项相关及其应用杭州商学院李金昌社会经济按变量的性质不同可分为两类：一类是其变量可以用具体数值表示它们之间的相关关系，如人均收入与食品支出之间的相关等，称之为数值变量相关；另一类是其变量不能或不完全能用具体数值表示它们之间的相关关系，如是否为文盲与是...     

主成分分析与技术开发水平的综合评价

目前,河北省在考察技术开发水平时,采用了技术开发机构、人员构成、经费收支、项目情况等6项指标,而每一项指标内又包括若干项子指标,如经费收支包括上级拨款、专项贷款、企业自筹款等10项子指标。1988年,反映我省大中型企业技术开发水平的共有60个指标,1020个数据。由于这些指标之间存在着相关关系,所以给综合评价工作带来很大困难。怎样才能用几个新的、无关的变量来取代原来众多的相关变量,并且使这些变量尽可能全面地反映原问题的信息量,这就是主成分分析所要解决的问题。     

再谈确定性变量与随机变量

再谈确定性变量与随机变量江苏仪征市统计局朱庆元一般的统计学原理教材提出：变量按性质可分为确定性变量与随机变量两种。笔者至今不很明白，提出这个问题到底要说明什么。近来，一些统计学者提出，确定性变量也是随机变量，只是它们出现的概率为１００％。提出这种说法...     

我国劳动力市场失业回滞现象初探

经济模型是经济理论的数学表述.在经济模型中各经济变量之间的关系往往被描述成一一对应的函数形式.一些重要的经济变量之间的关系并不是一一对应的,这些变量的大小既取决于其他变量的影响,又取决于这些变量的运动方向和初始状态.     

运用因子载荷阵分组变量的新主成分法及其应用

文章提出了R型-因子分析法有得分函数与命名不一致且不符合实际、正交因子间完全线性无关、综合得分函数难分重要因子的变量、片面以信息量衡量各因子相对重要性等缺陷,提出运用因子载荷阵分组变量的新主成分法,并以我国区域产业素质水平为例,得到综合变量命名清晰,得分函数意义清晰并与命名一致,得分值更具实际意义,变量系数可检验指标体系和考察各变量相对重要性,此法可找重要综合因素,从中发现和解决问题等结论。     

网络文化对高校校园文化的影响——基于结构方程模型的分析

针对目前高校网络迅速发展的现状,在大量问卷调查的基础上,利用结构方程模型分析了网络文化对高校校园文化的影响。选择网络文化与高校校园文化为潜变量,网络意识文化、网络制度文化、网络物质文化、校园精神文化、校园物质文化为可测变量。通过对各可测变量之间的关系进行统计分析,得出网络文化能够对高校校园文化产生重要影响的结论,为促进网络文化与校园文化的共同发展提供了理论依据。     

谈辅助变量在抽样调查中的重要作用

在抽样调查中，变量按具体作用可分为调查变量和辅助变量两种。调查变量是指要估计的变量，如在农村经济抽样调查中，要估计粮食总产量，农村住户总收入等指标，这里粮食产量和农村住户收入就是调查变量。辅助变量指为提高调查的估计精度在抽样调查或估计阶段引入的其他变量，比如，以农村住户作为抽样单元，通过住户的人均收入和总人口来估计农村住户的总收入，人口数就是辅助变量。     

The exact distribution and density functions of a pre-test estimator of the error variance in a linear regression model with proxy variables

We consider a linear regression model when some independent variables are unobservable, but proxy variables are available instead of them. We derive the distribution and density functions of a pre-test estimator of the error variance after a pre-test for the null hypothesis that the coefficients for the unobservable variables are zeros. Based on the density function, we show that when the critical value of the pre-test is unity, the coverage probability in the interval estimation of the error variance is maximum.     

Semiparametric estimation of employment duration models

There are a variety of economic areas, such as studies of employment duration and of the durability of capital goods, in which data on important variables typically are censored. The standard techinques for estimating a model from censored data require the distributions of unobservable random components of the model to be specified a priori up to a finite set of parameters, and misspecification of these distributions usually leads to inconsistent parameter estimates. However, economic theory rarely gives guidance about distributions and the standard estimation techniques do not provide convenient methods for identifying distributions from censored data. Recently, several distribution-free or semiparametric methods for estimating censored regression models have been developed. This paper presents the results of using two such methods to estimate a model of employment duration. The paper reports the operating characteristics of the semiparametric estimators and compares the semiparametric estimates with those obtained from a standard parametric model.     

Approximating Fisher's information for the functional measurement error model

For the functional measurement error model, the true, unobservable explanatory variables when treated as nuisance parameters yield an increase in the number of nuisance parameters corresponding to an increase in sample size. Fisher's information may not exist for all parameters under this scenario. We propose a simple but effective method of deriving Fisher's information by approximating the design matrix of explanatory variables with a quantile design matrix. We illustrate the application of our method with a numerical example. Adaptation of this method shows very good performance for the prediction problem.     

Robust linear mixed models for Small Area Estimation

Hierarchical models are popular in many applied statistics fields including Small Area Estimation. One well known model employed in this particular field is the Fay–Herriot model, in which unobservable parameters are assumed to be Gaussian. In Hierarchical models assumptions about unobservable quantities are difficult to check. For a special case of the Fay–Herriot model, Sinharay and Stern [2003. Posterior predictive model checking in Hierarchical models. J. Statist. Plann. Inference 111, 209–221] showed that violations of the assumptions about the random effects are difficult to detect using posterior predictive checks. In this present paper we consider two extensions of the Fay–Herriot model in which the random effects are assumed to be distributed according to either an exponential power (EP) distribution or a skewed EP distribution. We aim to explore the robustness of the Fay–Herriot model for the estimation of individual area means as well as the empirical distribution function of their ‘ensemble’. Our findings, which are based on a simulation experiment, are largely consistent with those of Sinharay and Stern as far as the efficient estimation of individual small area parameters is concerned. However, when estimating the empirical distribution function of the ‘ensemble’ of small area parameters, results are more sensitive to the failure of distributional assumptions.     

Shared frailty models based on reversed hazard rate for modified inverse Weibull distribution as baseline distribution

The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared gamma frailty model and the inverse Gaussian frailty model with the reversed hazard rate. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin data set and a better model is suggested.     

Parameter identifiability in a class of random graph mixture models

We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are independent random variables when conditioned on the groups of the nodes being connected. In the binary random graph case, in which edges are either present or absent, these models are known as stochastic blockmodels and have been widely used in the social sciences and, more recently, in biology. Their generalizations to weighted random graphs, either in parametric or non-parametric form, are also of interest. Despite these many applications, the parameter identifiability issue for such models has only been touched upon in the literature. We give here a thorough investigation of this problem. Our work also has consequences for parameter estimation. In particular, the estimation procedure proposed by Frank and Harary for binary affiliation models is revisited in this article.     

A Comparison of Methods for Analysing a Nested Frailty Model to Child Survival in Malawi

Demographic and Health Surveys collect child survival times that are clustered at the family and community levels. It is assumed that each cluster has a specific, unobservable, random frailty that induces an association in the survival times within the cluster. The Cox proportional hazards model, with family and community random frailties acting multiplicatively on the hazard rate, is presented. The estimation of the fixed effect and the association parameters of the modified model is then examined using the Gibbs sampler and the expectation–maximization (EM) algorithm. The methods are compared using child survival data collected in the 1992 Demographic and Health Survey of Malawi. The two methods lead to very similar estimates of fixed effect parameters. However, the estimates of random effect variances from the EM algorithm are smaller than those of the Gibbs sampler. Both estimation methods reveal considerable family variation in the survival of children, and very little variability over the communities.     

A semi‐Markov model for binary longitudinal responses subject to misclassification

The authors propose a two‐state continuous‐time semi‐Markov model for an unobservable alternating binary process. Another process is observed at discrete time points that may misclassify the true state of the process of interest. To estimate the model's parameters, the authors propose a minimum Pearson chi‐square type estimating approach based on approximated joint probabilities when the true process is in equilibrium. Three consecutive observations are required to have sufficient degrees of freedom to perform estimation. The methodology is demonstrated on parasitic infection data with exponential and gamma sojourn time distributions.     

Correlation analysis with additive distortion measurement errors

This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a additive fashion by an observed confounding variable. Two estimators, a direct-plug-in estimator and a residual-based estimator, are proposed. Their asymptotical results are obtained, and the residual-based estimator is shown asymptotically efficient. Moreover, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the confidence interval. The empirical likelihood statistic is shown to be asymptotically chi-squared. Simulation studies are conducted to examine the performance of the proposed estimators. These methods are applied to analyse the Boston housing price data for an illustration.     

The determinacy of the regression factor score predictor based on continuous parameter estimates from categorical variables

The estimation of population parameters of the continuous common factor model from categorical observed variables is meanwhile regularly performed. It is shown that the formula for the calculation of the determinacy of the regression factor score predictor from the estimated model parameters has to be adapted under these conditions. A method for the calculation of this determinacy from the model parameters of the continuous population factor model based on categorical variables is proposed and evaluated by means of simulated population data. It turns out that using the uncorrected formula can lead to serious overestimation of determinacy for categorical variables.