The Relative Effectiveness of Procedures Commonly Used in Multiple Regression Analysis for Dealing with Missing Values

Expressions are derived for the bias and variance associated with procedures frequently used to estimate partial regression coefficients in a linear model having the two explanatory variables x ₁ and x ₂, with missing values on x ₂ only. The expressions are used to help gain insight into the relative effectiveness of these procedures for handling more complex patterns of missing data.     

Reverse Regression,Fairness, and Employment Discrimination

Possible salary discrimination can be studied by comparing mean salaries of, say, males and females, after statistical adjustment for differences in job qualifications. The adjustment is often made by regression, with salary as dependent variable, and job qualifications and sex as independent variables. One might also regress job qualifications on salary and sex, a procedure called reverse regression. Ideas about fairness as well as technical concepts are relevant to discrimination studies. There are two distinct aspects of fairness, one based on comparisons of salary and the other based on comparisons of qualifications. Both concepts are needed to evaluate fairness.     

Logistic Regression and Discriminant Analysis by Ordinary Least Squares

If the observations for fitting a polytomous logistic regression model satisfy certain normality assumptions, the maximum likelihood estimates of the regression coefficients are the discriminant function estimates. This article shows that these estimates, their unbiased counterparts, and associated test statistics for variable selection can be calculated using ordinary least squares regression techniques, thereby providing a convenient method for fitting logistic regression models in the normal case. Evidence is given indicating that the discriminant function estimates and test statistics merit wider use in nonnormal cases, especially in exploratory work on large data sets.     

Utilizing the Flexibility of the Epsilon-Skew-Normal Distribution for Common Regression Problems

In this paper we illustrate the properties of the epsilon-skew-normal (ESN) distribution with respect to developing more flexible regression models. The ESN model is a simple one-parameter extension of the standard normal model. The additional parameter ~ corresponds to the degree of skewness in the model. In the fitting process we take advantage of relatively new powerful routines that are now available in standard software packages such as SAS. It is illustrated that even if the true underlying error distribution is exactly normal there is no practical loss n power with respect to testing for non-zero regression coefficients. If the true underlying error distribution is slightly skewed, the ESN model is superior in terms of statistical power for tests about the regression coefficient. This model has good asymptotic properties for samples of size n>50.     

The Use of Polynomials to Shift Coefficients in Linear Regression Models

Polynomials are commonly used in linear regression models to capture nonlinearities in explanatory variables. It is less common, however, that polynomials are used to shift the regression coefficients, an exception being the use of polynomially distributed lag coefficients. This note recommends the technique for a wider range of applications and suggests the Lagrangian interpolation representation as the most convenient for practitioners.     

Method of Moments Estimation in Linear Regression with Errors in both Variables

Recently, in this journal, there has been revised attention on estimating the parameters of the errors in variables, linear structural model. For example, O’Driscoll and Ramirez (2011) used a geometric approach to give insight into the performance of various slope estimators for the linear structural model as introduced by the present author. This article aims to provide a unified method of moments approach for estimating the parameters in the linear structural model, concentrating attention on estimators using the higher moments, which to date has received only little attention in the literature.     

Pay equity: The role and limitations of statistical analysis

Regression is the method of choice for analyzing complex salary structures, such as those of university faculty. Unfortunately, not only are there limitations on the data available and shortcomings in the method, but courts do not always understand the evidence presented to them. Statistical analysis can play an important role in uncovering discrimination, but caution is necessary in analysis and presentation.     

Empirical Likelihood Based Synthetic Data Method for Censored Regression Analysis

In this article, we propose a new empirical likelihood method for linear regression analysis with a right censored response variable. The method is based on the synthetic data approach for censored linear regression analysis. A log-empirical likelihood ratio test statistic for the entire regression coefficients vector is developed and we show that it converges to a standard chi-squared distribution. The proposed method can also be used to make inferences about linear combinations of the regression coefficients. Moreover, the proposed empirical likelihood ratio provides a way to combine different normal equations derived from various synthetic response variables. Maximizing this empirical likelihood ratio yields a maximum empirical likelihood estimator which is asymptotically equivalent to the solution of the estimating equation that are optimal linear combination of the original normal equations. It improves the estimation efficiency. The method is illustrated by some Monte Carlo simulation studies as well as a real example.     

缺失数据下的逆概率多重加权分位回归估计及其应用

数据缺失问题普遍存在于应用研究中。在随机缺失机制假定下,本文从模型推断角度出发,针对线性缺失分位回归模型,提出一种新的有效估计方法——逆概率多重加权（IPMW）估计。该方法是在逆概率加权（IPW）估计的基础上,结合倾向得分匹配及模型平均思想,经过多次估计,加权确定最终参数估计结果。该方法适用于响应变量是独立同分布或独立非同分布的情形,并适用于绝大多数缺失场景。经过理论推导及模拟研究发现,IPMW估计量在继承IPW估计量的优势上具有更稳健的性质。最后,将该方法应用于含有缺失数据的微观调查数据中,研究了经济较发达的准一线城市中等收入群体消费水平的影响因素,对比两种估计方法的估计结果及置信带,发现逆概率多重加权估计量的标准偏差更小,估计结果更稳健。     

An evaluation of the reconstructed coefficient of determination and potential adjustments

Previously, a method was proposed for calculating a reconstructed coefficient of determination in the case of right-censored regression using the expectation–maximization (EM) algorithm. This measure is assessed via simulation study for the purpose of evaluating the utility of model fit. Further, several reconstructed adjusted coefficients of determination are proposed and compared via simulation study for the purpose of model selection. The application of these proposed measures is illustrated on a real dataset.     

Bayesian Analysis of Least Absolute Relative Error Regression

In an important article by Chen et al. (2010) introduced a new distribution compatible with maximum likelihood estimation in a Least Absolute Relative Error (LARE) setting. In this article, we show first that the posterior of the model is log – concave and thus specialized and highly efficient techniques can be used to perform Bayesian inference without the use of MCMC since they provide independent draws from the posterior. Second, we approximate the distribution using a finite mixture of normals. Surprisingly, the log-LARE distribution can be approximated using a finite scale mixture of normals with few components.     

基于尾部指数回归方法的CVaR估计以及实证研究

 在险价值VaR是一种非常重要的金融风险度量方法,近期也有很多关于动态VaR以及条件VaR (CVaR) 等方面的研究。根据金融资产的收益率具有重尾特征这一事实,本文假定金融资产收益率服从重尾分布,并假定重尾分布的尾部指数随着收益率发生变化。本文基于尾部指数回归模型对重尾分布的尾部指数进行估计,进而得到收益率尾部数据所服从的条件分布,并首次运用该方法对条件VaR进行估计。本文对沪深300指数进行了实证研究,得到CVaR的估计,并对估计得到的CVaR的预测效果作出检验,并与传统VaR估计方法进行了对比,实证结果发现本文的方法的预测效果更好。     

The ubiquitous angle

Summary.  Previously we used the geometry of n -dimensional space to derive the paired samples t -test and its p -value. In the present paper we describe the 'ubiquitous' application of these results to single degree of freedom linear model hypothesis tests. As examples, we derive the p - and t -values for the independent samples t -test, for testing a contrast in an analysis of variance and for testing the slope in a simple linear regression analysis. An angle θ in n -dimensional space is again pivotal in the development of the ideas. The relationships between p , t , θ , F and the correlation coefficient are also described by using a 'statistical triangle'.     

The application of generalized ridge and stein-like general minimax rules to multicollinear data

We consider the use of minimax shrinkage estimators for the linear regression mcjel under several loss functions when severe multicollinearity is present. The examples considered illustrate that little or no departure from the least squares estimates is permitted in many cases when the data is highly multicollinear and/or shrinkage is toward a point in the parameter space that does not closely agree with the sample data     

Regression analysis of restricted mean survival time based on pseudo-observations for competing risks data

Competing risks data often occur in many medical follow-up studies. When the survival time is the outcome variable, the restricted mean survival time has heuristic and clinically meaningful interpretation. In this article, we propose a class of regression models for the restricted mean survival time in the competing risks setting. We adopt a technique of pseudo-observations to develop estimating equation approaches for the model parameters and establish asymptotic properties of the resulting estimators. The finite-sample behavior of the proposed method is evaluated through simulation studies, and an application to the Women’s Interagency HIV Study is provided.     

模糊数据的回归模型结构分析

本文在给出对称三角模糊数样本基础上,提出模糊数据回归分析模型的一般结构。在使用线性规划LP方法进行模糊回归系数估计时,根据模糊集合的择近原则,给出了利用样本平均贴近度评价模型拟合效果的一个准则。通过实例计算,比较了模糊样本回归模型未知参数估计的FLP方法和FLS 方法。     

基于分位回归的国家形象影响因素分析

国家形象是国家软硬实力的综合体现,对于一国在国际舞台的表现有着重要影响。现实中存在许多影响国家形象的因素。本文从国际竞争力的概念和数据出发,通过对世界主要国家和地区的国家形象的影响因素做出实证分析研究。利用洛桑国际管理发展学院（IMD）的国际竞争力数据库中关于国家形象指标的数据,我们采用分位回归方法,以揭示造成不同国家形象水平的客观影响因素,并与普通最小二乘回归结果进行对比,从而得到更全面的信息,为提高我国的国家形象提供实证依据。     

On Permutation Tests in Multiple Regression and Analysis of Covariance Problems

We introduce distribution-free permutation tests and corresponding estimates for studying the effect of a treatment variable x on a response y. The methods apply in the presence of a multivariate covariate z. They are based on the assumption that the treatment values are assigned randomly to the subjects.     

中国广义回归抽样估计系统的构建及应用

在抽样理论和应用研究方面,中国一直比较重视抽样方案设计,而忽视抽样估计方法研究。本文在系统总结加拿大等西方国家成功经验的基础上,引入并改进了一套广义回归估计系统,应用在复杂的连续多阶抽样调查中。本文以各类常见的抽样设计为基础,通过模型组和模型水平将现有的超总体模型进行扩展,建立各种类型的回归模型进行模型辅助的广义回归估计,最终形成一套广义回归估计系统,为中国抽样估计的应用研究奠定理论基础。最后,本文以中国农产量的连续多阶抽样调查为例,给出了具体的回归估计程序,从而验证这套系统的实践性和应用价值。