交叉熵方法理论上的缺陷及其改进研究

本文针对传统交叉熵（CE）方法在平衡和更新社会核算矩阵（SAM）研究中存在的缺陷进行分析,提出了基于离差熵绝对值期望最小化的改进模型1和基于离差熵平方期望最小化的改进模型2。理论结果表明：传统的CE方法得到的解是本文所提出的基于离差熵绝对值期望最小化改进模型1的一种特殊情况。同时为检验模型改进前后的实际效果,本文运用蒙特卡罗方法进行模拟分析,模拟结果表明：改进后的模型2得到的SAM流量矩阵精度比传统的CE方法得到的精度更高,而改进后的模型1得到的精度却相对较低。     

社会核算矩阵及其平衡方法研究

社会核算矩阵(SAM)是国民经济核算的一种重要形式,由于其数据来源多样且数据依赖于统计时间,这就决定了必须找到一个比较科学的方法对社会核算矩阵进行数据的调整与平衡。RAS方法与交叉熵(CE)方法是应用较为广泛的两种方法。本文通过比较研究认为,RAS方法是CE方法的一个特例———最小交叉熵模型,而CE方法是RAS方法的一般化,二者在实践应用过程中的取舍取决于研究者研究的侧重点。理论研究表明,当研究者侧重研究名义流的变化时,无疑RAS方法是首选;而当我们拥有各方面的信息来源并且用于结构变化的分析时,无疑CE方法是首选。但二者在实际研究中的优度比较仍是值得研究的问题。     

投入产出表和社会核算矩阵更新研究评述

本文对投入产出(IO)表和社会核算矩阵(SAM)更新方法进行了归类和比较评述。主要观点:第一,已有的IO表或SAM更新方法主要分为统计学方法、优化法和宏观经济学分析方法;第二,以现代经济学为基础的更新技术应引起高度重视;第三,在非普查年份,统计部门应制度化地开展重点IO系数调查,并将相关数据及时公开化;第四,在实际操作中应正确认识更新中已知信息的地位,并注意更新中的保号性问题。     

SAM乘数效应链接模型设计与应用研究

目前国内外对投入产出模型的研究已经成熟,但如何将其扩展到整个国民经济收入分配和金融领域,还没有特别成熟的模型。有人尝试在社会核算矩阵（Social Accounting Matrix,SAM）上建立投入产出模型,但其应用的灵活性会受到限制。本文将SAM流量矩阵划分为投入产出表、国民收入流量表、金融流量表三张表,先分别建立三个模型,然后将其链接起来,形成一个能够反映国民经济所有环节乘数关系的模型系统。然后利用中国2012年的SAM数据,举例说明了其在实际经济分析中的应用。     

随机存放点和体积下拣货路径问题研究

针对货物存放点和货物体积的不确定性,提出应用交叉熵法解决拣货车路径问题的方法,由于目标函数的复杂性,设计一种基于Monte-Carlo抽样求解路径期望距离的有效方法.为了提高标准交叉熵(CE)法的性能,设计了随分位值大小发生变化的更新Markov转移矩阵关键路径的自适应调整算法.计算结果验证了采用该方法解决此间题的鲁棒性和有效性.     

经济核算类矩阵调整的JSD方法及扩展研究

现有的矩阵更新、平衡等调整方法多存在两种缺陷：一是度量新旧矩阵间差异的函数形式不对称,并非严格“距离”概念;二是要求矩阵元素非负导致使用范围受限。为改进上述不足,本文提出了包括Jensen–Shannon divergence（JSD）在内的若干基于对称距离优化的新方法,并统一进行保号、误差妥协等扩展以方便实际运用。在此基础上本文利用中国及其他28个国家的数据,对比分析了多种矩阵调整方法的实际效果,结果发现：第Ⅰ类JSD方法表现最突出且相对稳健,值得代替现在使用较广泛的RAS或交叉熵方法。     

基于GDP水平的区域技术创新效率测度

区域技术创新效率是区域发展的动力,是衡量区域技术创新运营机制有效程度的重要标准,反应一个地区的研发水平和投入资源的利用率。通过建立区域技术创新效率指标体系,根据2009年我国30个省、市、自治区人均GDP构造系数矩阵,确定区域间的竞合关系;应用带有系数矩阵的交叉效率模型对2009年我国30个省、市、自治区的技术创新效率进行测度得出交叉效率矩阵,最后应用熵值法确定权重并得出最终效率。实证结果表明全部30个地区的技术创新效率均具有提升空间,该方法可以对所有区域进行充分排序且与传统仁慈型和进取型交叉效率方法相比更符合实际情况。     

我国银行系统性风险传染的风险估测

近年来的金融危机凸显了评估一个国家或地区系统性风险传染效应的紧迫性和重要性,是否存在系统性风险成为衡量金融安全的一个重要方面。本文利用矩阵法构建我国银行的风险传染模型,用最小二乘法和相对熵两种方法分析了不同损失水平下单家银行倒闭可能引起的系统性风险传染。结果表明:最小二乘方法下的风险敞口矩阵更符合实际;2005年的银行风险传染过程会发生一到二轮,且受到负面影响的主要是股份制银行;由于银行核心资本的提高,2009年的风险传染则几乎不会发生。     

投入产出表、社会核算矩阵的更新方法研究

本文将现有的众多矩阵更新技术纳入约束最优化的数学建模框架中,并统一进行了若干扩展,特别地,在约束条件存在冲突时通过引入误差精度调整项,使得原本不可行的矩阵更新问题能够求解,以扩大其适用范围。然后使用中国2002年和2007年的投入产出表对6种扩展修正后的矩阵更新方法进行了实证比较,结果显示无论是基于流量还是基于系数形式,或是对矩阵进行聚合处理,更新矩阵时ERAS的表现始终是最优的,ENSD其次,两者差距较小;而EAD方法表现较差。     

最小二乘法在新校区场地平整优化设计中的应用

新校区场地平整设计中,常用的方法已经无法满足工程设计的精度要求,而采用最小二乘法能够实现场地平整的优化设计,使平整场地设计接近于客观实际,能使填挖实现基本平衡,工程量得到合理控制,节省平整场地的工程投资。     

Updating and Estimating a Social Accounting Matrix Using Cross Entropy Methods

The problem in estimating a social accounting matrix (SAM) for a recent year is to find an efficient and cost-effective way to incorporate and reconcile information from a variety of sources, including data from prior years. Based on information theory, the paper presents a flexible 'cross entropy' (CE) approach to estimating a consistent SAM starting from inconsistent data estimated with error, a common experience in many countries. The method represents an efficient information processing rule-using only and all information available. It allows incorporating errors in variables, inequality constraints, and prior knowledge about any part of the SAM. An example is presented, applying the CE approach to data from Mozambique, using a Monte Carlo approach to compare the CE approach to the standard RAS method and to evaluate the gains in precision from utilizing additional information.     

On the relative efficiency of estimators which include the initial observations in the estimation of seemingly unrelated regressions with first-order autoregressive disturbances

The generalized least squares estimator for a seemingly unrelated regressions model with first-order vector autoregressive disturbances is outlined, and its efficiency is compared with that of an approximate generalized least squares estimator which ignores the first observation. A scalar index for the loss of efficiency is developed and applied to a special case where the matrix of autoregressive parameters is diagonal and the regressors are smooth. Also, for a more general model, a Monte Carlo study is used to investigate the relative efficiencies of various estimators. The results suggest that Maeshiro (1980) has overstated the case for the exact generalized least squares estimator, because, in many circumstances, it is only marginally better than the approximate generalized least squares estimator.     

Variable selection via composite quantile regression with dependent errors

We propose composite quantile regression for dependent data, in which the errors are from short‐range dependent and strictly stationary linear processes. Under some regularity conditions, we show that composite quantile estimator enjoys root‐n consistency and asymptotic normality. We investigate the asymptotic relative efficiency of composite quantile estimator to both single‐level quantile regression and least‐squares regression. When the errors have finite variance, the relative efficiency of composite quantile estimator with respect to the least‐squares estimator has a universal lower bound. Under some regularity conditions, the adaptive least absolute shrinkage and selection operator penalty leads to consistent variable selection, and the asymptotic distribution of the non‐zero coefficient is the same as that of the counterparts obtained when the true model is known. We conduct a simulation study and a real data analysis to evaluate the performance of the proposed approach.     

Adjustment of Input–Output Tables from Two Initial Matrices

The compilation of the information required to construct survey-based input–output (I–O) tables consumes resources and time to statistical agencies. Consequently, a number of non-survey techniques have been developed in the last decades to estimate I–O tables. These techniques usually depart from observable information on the row and column margins, and then the cells of the matrix are adjusted using as a priori information a matrix from a past period (updating) or an I–O table from the same time period (regionalization). This paper proposes the use of a composite cross-entropy approach that allows for introducing both types of a priori information. The suggested methodology is suitable to be applied only to matrices with semi-positive interior cells and margins. Numerical simulations and an empirical application are carried out, where an I–O table for the Euro Area is estimated with this method and the result is compared with the traditional projection techniques.     

Robust estimation procedures and visual display techniques for a two-way classification model

An important problem in statistics is to study the effect of one or two factors on a dependent variable. This type of problem can be formulated as a regression problem (by using dummy (0,1) variables to represent the levels of factors) and the standard least squares (LS) analysis is well-known. The least absolute value (LAV) analysis is less well known, but certainly is becoming more widely used, especially in exploratory data analysis.The purpose of this report is to present a didactic treatment of visual display methods useful in exploratory data analysis. These visual display techniques (stem- and- leaf, box- and- whisker, and two-way plots) are presented for both the least squares and the least absolute value analyses of a two-way classification model.     

Relative Home‐Court Advantage: The Impact of Travel on Team Production When One Team is Closer than its Opponent to a Neutral Game Site

Using data from the National Collegiate Athletic Association Men's Basketball Tournament, I examine the impact of travel on team production in a setting where one team is geographically closer than its opponent to a neutral site. I hypothesize and find that the closer team, or relative home team, has a relative home‐court advantage that helps it to out‐produce its opponent. When the relative home team travels a much shorter distance than its opponent to a neutral site, binary logistic and ordinary least squares regressions indicate a positive relationship between relative home‐court advantage and, respectfully, winning and margin of victory. Copyright © 2015 John Wiley & Sons, Ltd.     

New Nonlinear Approaches for the Adjustment and Updating of a SAM

Many structural relationships should be taken into account in any reasonable adjustment and updating process. These structural relationships are mainly represented by ratios of different types, such as technical coefficients or the proportion of the cell value in relation to its row or column total. We believe that in many cases (either because of lack of information or when the time elapsed for the estimation of a social accounting matrix is not long enough to allow for any significant structural change) the updating process should try to minimize the rela- tive deviation of the new coefficients from the initial ones in a homogeneous way. This homogeneity would mean that the magnitude of this relative deviation is similar among the elements of each row or column, therefore avoiding the concentration of the changes in particular cells of the SAM. In this work, we propose some new adjustment criteria in order to obtain a more homogeneous relative adjustment of the structural coefficients. These criteria combine the adjustment method proposed by Matuszewski et al. (1964) with other deviation functions. Each of the adjustment criteria proposed leads to a nonlinear optimization problem which is reformulated as a linear program. We test the usefulness of this proposal by comparing its results with the ones obtained by more standard approaches and we are able to show that these approaches tend to produce a less homogeneous pattern of coefficient adjustment, under certain circumstances, than the ones we put forward.     

解加权约束最小二乘问题的行M-不变方法

本文提出了一种新的求解加权约束线性最小二乘问题方法,即利用行M-不变矩阵得到了求解加权约束线性最小二乘的updating问题的递推方法。     

Another look at the naive estimator in a regression model

We consider the linear regression model where only a particular linear function of the dependent variables is observed, Stahlecker and Schmidt (1987) proposed a naive least squares (LS) estimator for regression coefficients in such a case. In this note we represent their estimator as a general ridge estimator. This observation leads to a view different from the previous work and provides an easy way of obtaining many important properties of the naive LS estimator. Our approach also gives some insight into the relationship between the naive LS estimator and the generalized least squares estimator.