Collapsibility of Conditional Graphical Models

Abstract. In this paper, we consider two kinds of collapsibility, that is, the model‐collapsibility and the estimate‐collapsibility, of conditional graphical models for multidimensional contingency tables. We show that these two definitions are equivalent, and propose a sufficient and necessary condition for them in terms of the interaction graph, which allows the collapsibility to be characterized and judged intuitively and conveniently.     

A Copula‐Based Non‐parametric Measure of Regression Dependence

Abstract. This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new non‐parametric measure of regression dependence and study its properties. Besides being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent non‐parametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of a small simulation study.     

分位回归、教育回报率与收入差距

本文简要回顾了新近出现的一些利用分位回归考察我国教育回报率和收入差距的文献。本文认为单纯利用分位回归中教育回报率的差异来考察教育对收入差距的影响的做法有待商榷;同时,在应用分位回归和报告回归结果的过程中区分“条件分布”和“无条件分布”是十分必要的。     

Quality of Fit Measures in the Framework of Quantile Regression

Abstract. In regression experiments, to learn about the strength of the relationship between a covariate vector and a dependent variable, we propose a ‘coefficient of determination’ based on the quantiles. Such a coefficient is a ‘local’ measure in the sense that the strength is measured at a prespecified quantile level. Once estimated, it can be used, for example, to measure the relative importance of a subset of covariates in the quantile regression context. Related to this coefficient, we also propose a new ‘local’ lack‐of‐fit measure of a given parametric model. We provide some asymptotic results of the proposed measures and carry out a Monte Carlo simulation study to illustrate their use and performance in practice.     

基于非对称分布散点分位数的区间数据回归分析

许多经济变量(如GDP)水平序列随着时间变化具有单调趋势,截面数据(如各地区GDP)之间存在差异,为了研究经济变量在一段时间内的平均发展水平和相互关系,文章基于区间型符号数据的研究视角,提出了一种基于分位数思想的Bayesian回归方法,用以分析内部存在非对称分布散点的区间数据,既可以估计数据的区间,也可以预测数据在此区间内的偏度和离散程度。在模拟研究中,通过对评价指标数值的假设检验分析了该模型相对于上、下限和中点半径模型的效果,并根据真实数据中存在异常信息的现象,在模拟数据中加入异常值,进一步验证分位数方法的优势和稳健性。在实证研究中,运用提出的分位数方法,上、下限法和中点半径法对我国各地区GDP和工业生产总值年度数据进行区间回归分析,评价指标显示分位数模型Bayesian方法具有更优的拟合和预测效果,在GDP发展水平不同的地区,工业增长的贡献存在差异。     

基于贝叶斯方法的比例数据分位数推断及其应用

为了尝试使用贝叶斯方法研究比例数据的分位数回归统计推断问题,首先基于Tobit模型给出了分位数回归建模方法,然后通过选取合适的先验分布得到了贝叶斯层次模型,进而给出了各参数的后验分布并用于Gibbs抽样。数值模拟分析验证了所提出的贝叶斯推断方法对于比例数据分析的有效性。最后,将贝叶斯方法应用于美国加州海洛因吸毒数据,在不同的分位数水平下揭示了吸毒频率的影响因素。     

Semiparametric Quantile Regression Analysis of Right‐censored and Length‐biased Failure Time Data with Partially Linear Varying Effects

Right‐censored and length‐biased failure time data arise in many fields including cross‐sectional prevalent cohort studies, and their analysis has recently attracted a great deal of attention. It is well‐known that for regression analysis of failure time data, two commonly used approaches are hazard‐based and quantile‐based procedures, and most of the existing methods are the hazard‐based ones. In this paper, we consider quantile regression analysis of right‐censored and length‐biased data and present a semiparametric varying‐coefficient partially linear model. For estimation of regression parameters, a three‐stage procedure that makes use of the inverse probability weighted technique is developed, and the asymptotic properties of the resulting estimators are established. In addition, the approach allows the dependence of the censoring variable on covariates, while most of the existing methods assume the independence between censoring variables and covariates. A simulation study is conducted and suggests that the proposed approach works well in practical situations. Also, an illustrative example is provided.     

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。