Semiparametric quantile modelling of hierarchical data

The classic hierarchical linear model formulation provides a considerable flexibility for modelling the random effects structure and a powerful tool for analyzing nested data that arise in various areas such as biology, economics and education. However, it assumes the within-group errors to be independently and identically distributed （i.i.d.） and models at all levels to be linear. Most importantly, traditional hierarchical models （just like other ordinary mean regression methods） cannot characterize the entire conditional distribution of a dependent variable given a set of covariates and fail to yield robust estimators. In this article, we relax the aforementioned and normality assumptions, and develop a so-called Hierarchical Semiparametric Quantile Regression Models in which the within-group errors could be heteroscedastic and models at some levels are allowed to be nonparametric. We present the ideas with a 2-level model. The level-1 model is specified as a nonparametric model whereas level-2 model is set as a parametric model. Under the proposed semiparametric setting the vector of partial derivatives of the nonparametric function in level-1 becomes the response variable vector in level 2. The proposed method allows us to model the fixed effects in the innermost level （i.e., level 2） as a function of the covariates instead of a constant effect. We outline some mild regularity conditions required for convergence and asymptotic normality for our estimators. We illustrate our methodology with a real hierarchical data set from a laboratory study and some simulation studies.     

非参数固定效应Panel Data模型的统计推断

本文主要讨论了非参数固定效应Panel data模型的估计与检验问题,首先我们利用Profile最小二乘方法得到了固定效应与非参数部分的估计;接着基于比较原假设与备择假设下模型拟合的残差平方和的思想针对固定效应的检验问题构造了检验统计量,并给出了计算检验p-值的F分布逼近法。     

基于面板分位回归方法的我国金融发展对城乡收入差距影响分析

在收入差距的不同分位点上,金融发展对其的影响会展现出不一样的特征。由于我国区域金融发展不均,这一作用机制还具有显著的地区差异。本文利用面板分位回归模型和面板数据聚类方法探寻金融发展对贫富分化作用的分位点特征和地区差异。实证表明,我国大部分地区的金融发展加剧城乡收入差距的扩大,并且这一作用机制存在动态变化特征。当城乡收入差距从高分位点变动到低分位点时,金融发展拉大城乡收入差距的作用逐渐减缓,部分省份甚至具有金融发展抑制城乡收入差距扩大的效应。本文的研究结论将为业内人士和政府的相关决策提供参考依据。     

中国居民消费的特征分析——中基于两阶段面板分位回归

本文结合实际问题,提出一种两阶段面板数据分位回归方法,并使用该方法分析我国居民的消费特征。通过横向和纵向比较揭示三种不同收入人群的边际消费倾向的变化趋势。文章认为中等收入者的边际消费倾向趋于稳定,低收入者和高收入者的边际消费倾向都有上升的趋势。中国居民的边际消费倾向呈现"U"型,所以提高低收入者的消费不仅在于提高他们的收入,更重要的是缩小当前的贫富差距。     

金融发展对经济增长影响的实证分析

本文将金融发展作为一个独立解释变量引入,构造经济增长的面板数据模型,运用面板数据以1994年为分界点分两阶段实证分析了全国及东、中、西部地区1985~2003年金融发展对经济增长的影响,以及东、中、西部地区影响的差异性,模型较好地拟合了数据。实证分析表明,各地区之间金融发展的不平衡性可以部分解释其经济增长的差异性。     

Hierarchical Bayesian models applied to air surveillance radars

Evaluation tests for air surveillance radars are often formulated in terms of the probability to detect a target at a specified range. Statistical methods applied in these tests do not explore all data in a full probabilistic model, which is crucial when dealing with small samples. The collected data are arranged longitudinally, in different levels (altitude), indexed both in time and distance. In this context we propose the application of dynamic Bayesian hierarchical models as an efficient way to incorporate the complete data set. Markov Chain Monte Carlo methods (MCMC) are used to make inference and to evaluate the proposed models.     

战略性新兴产业发展的金融支持研究

处于产业发展初期的战略性新兴产业,融资能力有限,如何融资成为影响其发展的关键性问题.战略性新兴产业的快速发展需要金融支持,银行贷款和证券融资是支持战略性新兴产业资金需求的主要方面.为此选取股票融资指标和银行贷款指标,借助面板数据模型,对金融支持我国七个战略性新兴产业的融资机制以及融资效率进行分析.     

一种面板数据分位数回归模型的工具变量方法

本文将工具变量分位数回归模型(IVQR)应用到面板数据中,结合Canay对面板分位数回归的两步估计法以及Chernozhukov对IVQR模型的估计方法,提出了两步面板分位数工具变量估计法(2S-IVFEQR),并给出相应的参数估计。本文提出的方法较已有的方法计算复杂度低,蒙特卡洛模拟结果显示在数据量不大或者处理长面板数据时,2S-IVFEQR方法要优于传统的IVFEQR方法,且运算时间短。     

Hierarchical linear regression models for conditional quantiles

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models, but it cannot deal effectively with the data with a hierarchical structure. In practice, the existence of such data hierarchies is neither accidental nor ignorable, it is a common phenomenon. To ignore this hierarchical data structure risks overlooking the importance of group effects, and may also render many of the traditional statistical analysis techniques used for studying data relationships invalid. On the other hand, the hierarchical models take a hierarchical data structure into account and have also many applications in statistics, ranging from overdispersion to constructing min-max estimators. However, the hierarchical models are virtually the mean regression, therefore, they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional covariates. Furthermore, the estimated coefficient vector (marginal effects) is sensitive to an outlier observation on the dependent variable. In this article, a new approach, which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models, is developed. On the theoretical front, we also consider the asymptotic properties of the new method, obtaining the simple conditions for an n1/2-convergence and an asymptotic normality. We also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.     

我国金融发展与城乡收人差距关系研究

我国城乡收入差距近几十年来持续拉大,城乡收入差距与金融发展之间存在着密切的关系,得到大多数学者的认同.从实证角度分析,利用全国30个省、直辖市、自治区35年的面板数据分别建立全国、东部、中部和西部的面板数据模型,结果显示金融发展与城乡收入差距存在着长期稳定的均衡关系,且金融发展规模显著拉大城乡收入差距,这种拉大效应在东中西部呈倒"U"型关系,我国并未出现拐点;金融发展效率的提高在我国整体及东中部地区能缩小城乡收入差距;城镇化仍然是引起我国城乡收入差距持续扩大的重要原因,我国还未进入发达国家城镇化提高能缩小城乡收入差距的拐点阶段.     

基于动态面板模型的中国城镇居民消费的研究

本文通过设定和估计动态面板数据模型,考察我国城镇不同收入阶层居民在食品、医疗保健、交通通讯、娱乐教育文化和居住方面消费的差异性,得出如下结论:城镇居民总消费变动表现出对收入变动的"过度敏感性",但不同收入阶层居民的敏感性是不同的,基本上是呈现"V"型的趋势,但上升的趋势不是特别明显,在各个层面的消费也表现出了不同的趋势。在总消费上不具有消费习惯,但低收入户在医疗保健上具有消费习惯,中等偏上户、高收入户、最高收入户在交通通讯方面具有消费习惯。     

多指标面板数据融合聚类分析

针对多指标面板数据的样品分类和历史时期划分问题,从多元统计分析理论角度提出一个多指标面板数据的融合聚类分析方法。该方法改进了多指标面板数据的因子分析和系统聚类方法,依据Fisher有序聚类理论,构造了Frobenius范数形式的离差平方和函数,提出了多指标面板数据的有序聚类方法。实证结果表明,该方法能够满足系统分析的统一性要求,保证指标之间的不相关;能够克服时间维度上均值处理造成的偏误,信息损失较少;能够解决面板数据有序聚类的问题;弥补了单一分析的片面性和局限性。     

面板数据交互固定效应模型的方差分量检验

研究了面板数据交互固定效应模型中方差分量的检验问题.首先依据模型中误差项的估计构造辅助回归模型,然后根据该辅助回归构造检验统计量,对模型中的异方差性进行检验.进一步,通过构造不同的辅助回归模型和检验统计量可以判别异方差的来源.在一定正则条件下,得到了检验统计量在原假设和备择假设下的渐近分布,并说明所提出的检验方法不依赖于误差分布.最后,通过模拟研究对本文的检验方法进行评价,说明所提检验方法是有效的.     

面板数据分位数回归模型求解的模式搜索法

本文应用最优化理论,对固定效应的面板数据分位数回归模型,提出一种模式搜索方法,此方法可以同时估计出所有分位点处的解释变量系数和所有个体的固定效应值。进一步利用蒙特卡洛模拟比较现有文献中涉及的面板数据分位数回归方法,结果显示无论误差项是否满足经典假设,模式搜索分位数回归法较之其他分位数回归估计方法更为有效.     

Optimal estimation in random coefficient regression models

In linear regression models with random coefficients, the score function usually involves unknown nuisance parameters in the form of weights. Conditioning with respect to the sufficient statistics for the nuisance parameter, when the parameter of interest is held fixed, eliminates the nuisance parameters and is expected to give reasonably good estimating functions. The present paper adopts this approach to the problem of estimation of average slope in random coefficient regression models. Four sampling situations are discussed. Some asymptotic results are also obtained for a model where neither the regressors nor the random regression coefficients replicate. Simulation studies for normal as well as non-normal models show that the performance of the suggested estimating functions is quite satisfactory.