国民核算中的指数序列问题研究

在国民核算和经济统计实践中,广泛运用多种价格指数和物量指数,其中最重要者莫过于生产指数(如GDP物量指数)和消费者价格指数(如CPI,即我国的居民消费价格指数)。这些指数可以选择不同的公式逐年编制,从而形成各种指数序列。SNA(1993)、麦卡锡(P.McCarthy,1999)、许宪春(2000)和施雷耶(P.Schreyer,2005)等先后对国民核算指数进行了专门研究。本文试图首先归纳和扩展指数序列的一般理论,进而探讨国民核算中有关指数编制与应用的若干问题。一、几种基本指数序列及其特征为便于讨论各种指数公式和指数序列,我们约定以下公式符号:记t时期j…     

基于BP神经网络的S＆P500指数期权定价

期权定价理论源于影响期权价格的变量和期权价格之间的非线性关系,传统的Black-Scholes期权定价公式过于严格的假设削弱了该公式在现实中的适用性,使其在理论与应用上均存在缺陷。因此,能够以任意精度近似复杂非线性系统的神经网络运用于期权定价。分别利用BP神经网络和Black-Scholes期权定价公式对S＆P 500指数看跌期权进行定价,实证结果表明BP神经网络的定价结果要优于Black-Scholes定价公式。     

区位支付能力理论的模型及应用

区位支付能力分析是住房支付能力研究的发展,其理论基础是城市竞价模型。该分析主要从选择位置和选择宜人性因素两个方面进行。在区位支付能力理论研究的基础上可以确定区位支付能力指数,以分析城市居住空间结构形成的机理。文章利用调研数据,对北京市进行了实证分析,计算了当前北京市购房者区位支付能力指数,并分析了不同区域、不同住房类型、不同收入的区位支付能力情况。     

关于费雪“理想指数”的几点思考

综合指数是总指数的一种形式，它是由两个总量指标对比形成的指数。综合指数编制中权数的选择问题，亦即同度量因素问题，在历来的指数理论中影响最大的有两个派别：一为拉斯佩雷斯指数理论，主张用基期权数；一为派许指数理论，主张用报告期权数。拉氏价格指数公式：拉氏物量指数公式：派氏价格指数公式：派氏物量指数公式：一、关于拉氏和派氏指数公式同度量因素的影响问题在综合指数的计算过程中，同度量因素不仅起着统一的计算尺度的作用，而且还起到了权衡各种商品相对重要地位的作用。因此选择的权数所属的时期不同、对同一组数据，拉…     

基于Zenga指数的不平等测度研究

Zenga指数是一种性质优良的新型不平等测度指数,在国际上有大量的理论探讨和广泛的实证应用,但在国内却没有受到足够的重视。从与基尼系数对比的视角,对该指数进行了系统的研究,探讨了Zenga指数与基尼系数间的数理联系,总结了其所满足的一系列测度特性,并基于CFPS微观调查数据,同时应用Zenga指数和基尼系数对中国居民家庭人均纯收入的不平等进行了测度对比分析。研究表明,与基尼系数相比,Zenga指数具有更多的优良特性,对低收入群体收入差距更敏感;与洛伦茨曲线相比,Zenga不平等曲线能展现关于不平等动态变化的更多细节,更适合围绕低收入群体进行不平等现状及相关政策效应分析;另外,Zenga指数独特的加和交叉分解特性可为认识不平等的结构提供更深层次的信息。     

对统计指数中几个问题的思考

指数方法的多样性和复杂性,本应使我们的统计学教科书写得非常的丰富多彩,对指数理论与方法做出系统而生动的阐述。然而,绝大多数的统计学教科书只是重点介绍L式数量综合指数和P式质量综合指数的编制原理,并以此为基础来介绍平均指数的编制。对指数的概念、偏误的阐述却不够充分,不甚完善,因此,我们应当在统计学教科书中加强指数理论与方法的阐述,让读者明白指数编制的基本思想,明白为什么要编制指数、如何选择指数公式以及如何发展与完善指数的理论与方法。     

北京市城乡居民收入差距测度及其分解

在北京市的发展过程中,城乡居民收入差距的拉大已成为经济进一步发展的障碍。文章应用国际上流行的城乡收入比、泰尔指数和MLD指数三个指标分别对北京市城乡居民收入差距进行了具体测度,都得到了大致相同的结论。同时利用泰尔指数和MLD指数的分解公式,计算出了北京市城乡收入差距在总体差距中的贡献份额,以及城乡居民收入差距的变动对整体居民收入差距变动的影响。     

分割指数构建的一种新方法

分割指数(Segregation Index)是度量群体分割程度的统计指标,其理论、方法和应用是西方学术界的研究热点,而国内目前较少有专门针对分割指数的系统介绍和研究。文章梳理了相关研究文献,介绍并分析了各种已有分割指数的构建方法及其性质,勾勒出一幅较为全面的研究图谱;提出并论证了一种新方法,在已有指数的基础上构建了相应的加权分割指数。最后,对2013—2017年我国城镇职工的行业分割情况进行了测算,例示了各种分割指数的应用,验证了加权分割指数应用的良好效果。     

关于因子商指数若干问题研究

文章对匈牙利经济学家、统计学家帕尔·科夫斯在其所著的《指数理论与经济现实》一书中提出的关于因子商指数的定义、作用及总体因子商指数与个体因子商指数的关系等问题提出了诸多疑问，提出了笔者的看法及建议     

大数据指数是否可以替代统计调查指数

2014年7月,澳盛银行首次将阿里巴巴系列指数纳入通胀观察标的,标志着大数据指数已经开始对传统的统计调查指数提出质疑和挑战。本文基于阿里巴巴aSPI指数和官方公布的CPI指数的比较研究,首次提出了aSPI指数显著优于CPI指数的一些基本特征;同时,通过实证分析对比了两种指数的同步性特征和分解性特征,即首先运用协整检验方法确定二者的同步性;其次通过EMD模型对二者进行序列分解,得出各自的波动成分和增长趋势;最后,在EMD对aSPI指数分解的基础上,通过Lasso回归估计了CPI指数。研究表明,随着对大数据研究的广泛性、科学性以及方法论和软件工具的进步,大数据指数对传统统计调查的佐证、补充乃至融合将会成为一种新趋势,通过实证、应用与发展,逐步产生新的CPI编制方法和分析体系,将是大数据指数理论和实践的根本出路。     

Correcting for regression dilution bias: comparison of methods for a single predictor variable

In an epidemiological study the regression slope between a response and predictor variable is underestimated when the predictor variable is measured imprecisely. Repeat measurements of the predictor in individuals in a subset of the study or in a separate study can be used to estimate a multiplicative factor to correct for this 'regression dilution bias'. In applied statistics publications various methods have been used to estimate this correction factor. Here we compare six different estimation methods and explain how they fall into two categories, namely regression and correlation-based methods. We provide new asymptotic variance formulae for the optimal correction factors in each category, when these are estimated from the repeat measurements subset alone, and show analytically and by simulation that the correlation method of choice gives uniformly lower variance. The simulations also show that, when the correction factor is not much greater than 1, this correlation method gives a correction factor which is closer to the true value than that from the best regression method on up to 80% of occasions. We also provide a variance formula for a modified correlation method which uses the standard deviation of the predictor variable in the main study; this shows further improved performance provided that the correction factor is not too extreme. A confidence interval for a corrected regression slope in an epidemiological study should reflect the imprecision of both the uncorrected slope and the estimated correction factor. We provide formulae for this and show that, particularly when the correction factor is large and the size of the subset of repeat measures is small, the effect of allowing for imprecision in the estimated correction factor can be substantial.     

Additional variables and adjusted estimates with arbitrary known variance-covariance structure

When additional variables are fitted in a linear model under arbitrary known variance-covariance struture, the extra sum of squares due to fitting the new variables and adjusted parameter estimates can be computed in an efficient manner without actually explicity fitting the entire augmented model. When the additional variables are specific dummy variables, downdating formulae are readily obtained, thus generatina methods which are well known for the linear model with variance-covariance structure σ²I. Two different methods to downdate a linear model are presented.     

A non-iterative posterior sampling algorithm for linear quantile regression model

In this article, a non-iterative posterior sampling algorithm for linear quantile regression model based on the asymmetric Laplace distribution is proposed. The algorithm combines the inverse Bayes formulae, sampling/importance resampling, and the expectation maximization algorithm to obtain independently and identically distributed samples approximately from the observed posterior distribution, which eliminates the convergence problems in the iterative Gibbs sampling and overcomes the difficulty in evaluating the standard deviance in the EM algorithm. The numeric results in simulations and application to the classical Engel data show that the non-iterative sampling algorithm is more effective than the Gibbs sampling and EM algorithm.     

A non-iterative posterior sampling algorithm for Laplace linear regression model

In this article, a non-iterative sampling algorithm is developed to obtain an independently and identically distributed samples approximately from the posterior distribution of parameters in Laplace linear regression model. By combining the inverse Bayes formulae, sampling/importance resampling, and expectation maximum algorithm, the algorithm eliminates the diagnosis of convergence in the iterative Gibbs sampling and the samples generated from it can be used for inferences immediately. Simulations are conducted to illustrate the robustness and effectiveness of the algorithm. Finally, real data are studied to show the usefulness of the proposed methodology.     

熵理论中熵及熵权计算式的不足与修正

简述了熵的概念和熵在社会科学中的应用,分析了熵理论中熵值及熵权传统计算式中存在的不足,提出了一种合理可行的修正方法,并对熵值及熵权计算式的修正进行了数学证明,有效地完善和发展了熵理论。     

Fourth-order moments of augmented arch processes

This paper is concerned with establishing the correspondence between the fourth- order moments structure and the parametric representation for augmented ARCH processes. In an introduction, the possible types of fourth-order moments are classified and some tentative interpretation for each class is given. Then, algebraic formulae are developed that permit the calculation of all fourth- order cross moments that are possibly non-zero within the AARCH class on the basis of known AARCH parameters. These formulae are useful for evaluating properties of estimated AARCH models, if estimation is conducted via maximum likelihood methods or approximations, and also for possible use in method-of-moments estimation.     

THE FUNDAMENTAL FORMULA OF BLASCHKE IN INTEGRAL GEOMETRY AND GEOMETRICAL PROBABILITY, AND ITS ITERATION, FOR DOMAINS WITH FIXED ORIENTATIONS

The so-called “principal formulae” of planar integral geometry are conventionally couched in terms of the “kinematic density”dxdydθ. Here a corresponding theory with respect to the “Lebesgue density”dxdy, that is with rotations suppressed, is developed. The only real difference is that the new “fundamental formula of Blaschke”contains a term depending upon the relative orientations of the two domains involved. In particular, the remarkable iteration property of these formulae carries over. The usual principal formulae follow as a corollary of the formulae given here, upon, averaging over orientations.     

The Copula Information Criteria

We derive two types of Akaike information criterion (AIC)‐like model‐selection formulae for the semiparametric pseudo‐maximum likelihood procedure. We first adapt the arguments leading to the original AIC formula, related to empirical estimation of a certain Kullback–Leibler information distance. This gives a significantly different formula compared with the AIC, which we name the copula information criterion. However, we show that such a model‐selection procedure cannot exist for copula models with densities that grow very fast near the edge of the unit cube. This problem affects most popular copula models. We then derive what we call the cross‐validation copula information criterion, which exists under weak conditions and is a first‐order approximation to exact cross validation. This formula is very similar to the standard AIC formula but has slightly different motivation. A brief illustration with real data is given.     

Sampling distribution after splitting experimental units

It has been a common practice to recommend one distribution for a large class of problems. An example is the use of the logarithmic distribution for count data - the point of concern in this paper is its recommendation without regard to the size of the experimental unit. References for this particular distribution go back to Fisher et al. [1943]. Look up Douglas [1980], Patil et al. [1984] and Kotz and Johnson [1985] to pick up additional references in this area -especially through sorting the data base of the American Mathematical Society. We will show a fallacy in this structure; provide a computer algorithm find the actual distributions; and then to check on the divisibility. The language used is APL2. But the users can make up their own programs.