我国能源消费与GDP关系的非参数回归分析

近年来中国的GDP与能源消耗不断增长,但二者的走势在不同时期存在显著的差异,这是传统的计量经济模型无法解释的.文章尝试将非参数估计理论引入到回归模型中来,通过建立非参数回归模型对我国GDP与能源消费总量之间的关系进行研究,并提出一些较为可行的建议.     

高校教师工资影响因素分析

文章以某地区若干高校教师月平均工资为研究对象,随机抽取500名教师为样本,对于一些定性的解释变量采用虚拟变量的形式与工资进行回归分析,通过拟合线性回归模型及对其参数和整体方程的检验,分析出年龄、学历、职务等定性的解释变量对高校教师工资的影响程度。     

非线性回归模型的线性变换和正交多项式回归

在非线性回归模型中,部分模型可以通过数据变换转化为线性模型进行研究,但这种转换有时会引起随机扰动项的变换,改变其假设条件,从而影响模型的准确性.文章引入非线性回归模型的线性变换方法和正交多项式回归方法,重点介绍了正交多项式回归方法;基于R语言软件,通过例子说明了非线性模型线性变换的局限性,并给出了正交多项式回归方法拟合非线性模型的具体应用.     

基于非参数回归的财政收入与经济增长关系实证分析

文章首先对已有文献中财政收入和经济增长的实证分析方法进行考察,发现现行的方法存在着一些限制和问题,非参数回归方法可以某种程度克服这些问题.因此,在对非参数回归方法进行介绍的基础上,对1953～2010年中国财政收入增长速度和GDP名义增长率之间关系了进行了非参数回归.回归结果表明:GDP名义增长率取值在比较正常的范围(0％-20％)内时,财政收入增长速度和GDP名义增长率之间近似于线性关系,超出这个范围,二者之间的关系具有非线性关系.     

基于虚拟变量回归与SARIMA组合模型的GDP预测

文章根据我国1992年至2015年的GDP季度数据,建立了虚拟变量回归(DVR)模型、SARIMA模型及其组合(DVR-SARIMA)模型,并进行了比较与分析,结果发现组合(DVR-SARIMA)模型的拟合效果最好,预测性能亦是最好,且利用组合(DVR-SARIMA)模型对我国未来的季度GDP进行了预测,以期对我国未来的总体经济增长情况做出合理的分析与判断.     

一种检验回归参数差异的新方法

对回归模型的参数进行比较是计量经济学研究的一个重要内容.文章提出了一种新的思路来对回归模型的参数的差异进行检验,该方法与一般人们所用的Wald统计量来检验的方法和使用虚拟变量的方法相比而言比较灵活,应用面较广,它既可以对同一个回归方程的不同参数的差异进行比较,也可以对两个解释变量个数不同的回归方程的不同参数进行比较,在一定程度上能够解决其他方法所不能够处理的问题.     

非参数异方差模型中条件回归函数的EM算法——基于农村食品消费与纯收入的实证研究

对非参数异方差模型中回归函数的EM算法进行研究,并基于EM算法得到了条件回归函数的估计。此外,通过对农村居民食品消费支出与纯收入关系的实证分析,说明了基于EM算法的估计方法比最小二乘估计方法的拟合效果更好,并对恩格尔系数进行了拟合,分析了其变化走势。     

物流需求预测模型构建

文章选取1993-2014年社会物流总额衡量物流需求,定量分析社会物流总额与GDP、物流总费用、固定资产投资和进、出口总额的关系.采用MATLAB软件进行编程模拟,构建了物流需求多元非线性组合回归预测模型.结果表明:多元非线性组合回归预测模型预测效果明显优于多元线性回归、指数平滑法、多项式拟合(2次)及非线性预测法(幂函数).     

Multinomial响应广义半参数回归模型及应用

在消费行为学领域经常碰到的离散选择数据就是Multinomial响应数据,此类数据通常采用Multinomial Logit线性回归模型来处理,不过如果回归变量中的一部分与对数机率向量间呈非线性关系,其余回归变量与对数机率向量间呈线性关系,就需要引入以对数机率向量为因变量的广义半参数回归模型来处理这类实际数据了.文章以一次手机用户生活形态调查数据为例,讨论了向量广义半参数回归模型在消费者行为研究中的应用.     

混合类型辅助变量下模型校准抽样估计研究

在超总体模型中,一般用于构建模型的辅助变量多为连续型变量,对混合类型辅助变量的模型研究较少.为了同时利用与研究变量相关的连续型和离散型辅助变量的信息,本文提出在模型校准的框架下,利用非参数核回归方法,得到混合类型辅助变量下的模型校准估计量.研究证明,该估计量是渐进设计无偏、设计一致和渐进正态的,并给出了估计量的方差和方差的估计量.数值模拟的结果显示,本文在总体回归函数为线性和非线性的情况下,估计效果均有所提高.此外,通过CLHLS数据的验证也表明该估计量的效果优于仅利用连续型辅助变量的估计量.     

Compound Regression and Constrained Regression: Nonparametric Regression Frameworks for EIV Models

Abstract

Errors-in-variable (EIV) regression is often used to gauge linear relationship between two variables both suffering from measurement and other errors, such as, the comparison of two measurement platforms (e.g., RNA sequencing vs. microarray). Scientists are often at a loss as to which EIV regression model to use for there are infinite many choices. We provide sound guidelines toward viable solutions to this dilemma by introducing two general nonparametric EIV regression frameworks: the compound regression and the constrained regression. It is shown that these approaches are equivalent to each other and, to the general parametric structural modeling approach. The advantages of these methods lie in their intuitive geometric representations, their distribution free nature, and their ability to offer candidate solutions with various optimal properties when the ratio of the error variances is unknown. Each includes the classic nonparametric regression methods of ordinary least squares, geometric mean regression (GMR), and orthogonal regression as special cases. Under these general frameworks, one can readily uncover some surprising optimal properties of the GMR, and truly comprehend the benefit of data normalization. Supplementary materials for this article are available online.     

Linearized Ridge Regression Estimator in Linear Regression

In this article, we aim to study the linearized ridge regression (LRR) estimator in a linear regression model motivated by the work of Liu (1993). The LRR estimator and the two types of generalized Liu estimators are investigated under the PRESS criterion. The method of obtaining the optimal generalized ridge regression (GRR) estimator is derived from the optimal LRR estimator. We apply the Hald data as a numerical example and then make a simulation study to show the main results. It is concluded that the idea of transforming the GRR estimator as a complicated function of the biasing parameters to a linearized version should be paid more attention in the future.     

A New Regression Model: Modal Linear Regression

The mode of a distribution provides an important summary of data and is often estimated on the basis of some non‐parametric kernel density estimator. This article develops a new data analysis tool called modal linear regression in order to explore high‐dimensional data. Modal linear regression models the conditional mode of a response Y given a set of predictors x as a linear function of x . Modal linear regression differs from standard linear regression in that standard linear regression models the conditional mean (as opposed to mode) of Y as a linear function of x . We propose an expectation–maximization algorithm in order to estimate the regression coefficients of modal linear regression. We also provide asymptotic properties for the proposed estimator without the symmetric assumption of the error density. Our empirical studies with simulated data and real data demonstrate that the proposed modal regression gives shorter predictive intervals than mean linear regression, median linear regression and MM‐estimators.     

Linearized Restricted Ridge Regression Estimator in Linear Regression

This article primarily aims to put forward the linearized restricted ridge regression (LRRR) estimator in linear regression models. Two types of LRRR estimators are investigated under the PRESS criterion and the optimal LRRR estimators and the optimal restricted generalized ridge regression estimator are obtained. We apply the results to the Hald data and finally make a simulation study by using the method of McDonald and Galarneau.     

New Ridge Regression Estimator in Semiparametric Regression Models

In the context of ridge regression, the estimation of shrinkage parameter plays an important role in analyzing data. Many efforts have been put to develop the computation of risk function in different full-parametric ridge regression approaches using eigenvalues and then bringing an efficient estimator of shrinkage parameter based on them. In this respect, the estimation of shrinkage parameter is neglected for semiparametric regression model. Not restricted, but the main focus of this approach is to develop necessary tools for computing the risk function of regression coefficient based on the eigenvalues of design matrix in semiparametric regression. For this purpose the differencing methodology is applied. We also propose a new estimator for shrinkage parameter which is of harmonic type mean of ridge estimators. It is shown that this estimator performs better than all the existing ones for the regression coefficient. For our proposal, a Monte Carlo simulation study and a real dataset analysis related to housing attributes are conducted to illustrate the efficiency of shrinkage estimators based on the minimum risk and mean squared error criteria.     

Nonlinear Regression

It is often thought that regression data should be mean-centered before being diagnosed for collinearity (ill conditioning). This view is shown not generally to be correct. Such centering can mask elements of ill conditioning and produce meaningless and misleading collinearity diagnostics. In order to assess conditioning meaningfully, the data must be in a form that possesses structural interpretability.     

Beta-Binomial回归模型及其应用

在成败型试验中或满意度支持率调查中,Beta-Binomial分布常被用来刻画具有偏大离差的计数型比例数据,由此提出Beta-Binomial回归模型,研究参数的最大似然估计方法并基于Newton-Raphson算法给出参数估计的迭代方法;重点讨论模型中回归参数和相关性参数存在的检验问题,提出Score检验方法并通过数值模拟研究Score检验统计量的检验功效问题;实例分析证明Beta-Binomial回归模型的有用性。     

Quadratic Programming and Penalized Regression

Quadratic programming is a versatile tool for calculating estimates in penalized regression. It can be used to produce estimates based on L ₁ roughness penalties, as in total variation denoising. In particular, it can calculate estimates when the roughness penalty is the total variation of a derivative of the estimate. Combining two roughness penalties, the total variation and total variation of the third derivative, results in an estimate with continuous second derivative but controls the number of spurious local extreme values. A multiresolution criterion may be included in a quadratic program to achieve local smoothing without having to specify smoothing parameters.     

Model Selection and Regression t-Statistics

It is shown that dropping quantitative variables from a linear regression, based on t-statistics, is mathematically equivalent to dropping variables based on commonly used information criteria.