Logistic模型多重共线性问题的诊断及改进

文章诊断并改进了logistic回归模型多重共线性问题方法,采用条件指数和方差分解比例两项指标进行共线性诊断、应用主成分改进和偏最小二乘回归两种方法进行多重共线性变量的改进处理:去除了回归模型中变量间的多重共线性影响,建立了较为理想的关系模型.结果表明,在Logisdc回归模型分析中,应用上述方法进行多重共线性的诊断和处理是有效及可行的.     

利用主成分回归法处理多重共线性的若干问题

在经济计量实践中,多重共线性是存在于线性经济计量模型中的一个普遍而需特别重视的问题.对于其解决方法,很多学者都进行了探讨.目前一些文献中颇有争议的是:利用主成分回归法处理多因素分析中多重共线性问题.     

局部线性估计中的多重共线性问题

各解释变量之间存在多重共线性是现实中很普遍的现象。本文对局部线性估计多重共线性问题进行了讨论,发现多重共线性造成局部线性估计精度下降的原因,并提出了一个补救方法:当变量之间高度相关时采用主成分回归可以有效提高估计精度。本文还通过模拟的方式证明了此方法的有效性。     

基于非线性-主成分Logistic回归的会计舞弊识别研究

混沌理论认为,人类行为大多具有非线性特征。会计舞弊属于行为会计的研究范畴,而传统上基于统计理论构建的舞弊识别模型大多受限于线性约束假设,可能存在模型设定偏误和信息提取不充分的缺陷。以沪深A股受到监管处罚的上市公司及其配对公司为样本,借鉴Taylor展开式的非线性思想,并使用主成分分析消除变量多重共线性,构建了非线性-主成分Logistic回归的会计舞弊识别模型。与线性回归模型对比发现,前者具有更高的舞弊识别正确率,模型拟合度更优。应用这一模型有助于更加充分提取舞弊识别信息,提高舞弊识别效率。     

基于主成分分析的汽车特征价格模型初探

特征价格模型建立过程中，特征变量的选取是一个重要问题。实证研究中，为消除特征变量问的多重共线性，研究者通常采用逐步回归分析法来筛选变量，这样进入模型的特征变量往往比较少。因此。本文将主成分分析法引入于特征价格模型。利用我国汽车数据，建立了基于汽车特征因素主成分分析的特征价格模型，不仅解决了汽车特征变量间存在的多重共线性问题，而且有效改善了用逐步回归分析法筛选变量选取较少变量的情形。     

基于粗集理论的线性回归方法及实证分析

通过分析实际问题中经济变量间往往出现多重共线性的现象，将粗集理论的约简思想引入线性回归分析，提出了基于粗集理论的线性回归模型来解决多重共线性问题，并通过实证分析来验证模型的可行性，为人们进行科学的预测和决策提供了一种新的思想和方法。     

一类新的多重共线性检验方法

解释变量间的相关性导致了多元线性回归模型的多重共线性问题,由于考察相关性的角度和方法不同,产生了不同的多重共线性的检验方法。由阿达马不等式可以构建多个变量的综合相关性度量指标,将该指标用于度量多元线性回归模型的解释变量的综合相关程度,用以作为多元线性回归模型多重共线性的一类检验方法。     

岭回归在资本结构影响因素回归建模中的应用

自多重共线性是资本结构影响因素线性回归模型中迫切需要解决的问题,本文运用岭回归方法,以医药制造类上市公司的统计资料为基础,对影响资本结构的主要因素进行了实证分析,有效地解决了回归模型中的多重共线性问题.     

多重共线性下的线性回归方法综述

多重共线性（简称共线性）是回归分析中一个非常棘手的问题。多重共线性由R．Frisch在1934年引入的，主要研究是在上世纪六、七十年代进行的，但直到现在仍然没有完全解决。     

基于聚类分析和因子分析消除多重共线性的方法

文章针对经典多元线性回归模型中存在的多重共线性问题,提出了一种新的基于聚类分析和因子分析的解决方法,并通过例子验证了此方法在实际应用中可以取得良好的效果。     

The Adaptive Gril Estimator with a Diverging Number of Parameters

We consider the problem of variables selection and estimation in linear regression model in situations where the number of parameters diverges with the sample size. We propose the adaptive Generalized Ridge-Lasso (\mboxAdaGril) which is an extension of the the adaptive Elastic Net. AdaGril incorporates information redundancy among correlated variables for model selection and estimation. It combines the strengths of the quadratic regularization and the adaptively weighted Lasso shrinkage. In this article, we highlight the grouped selection property for AdaCnet method (one type of AdaGril) in the equal correlation case. Under weak conditions, we establish the oracle property of AdaGril which ensures the optimal large performance when the dimension is high. Consequently, it achieves both goals of handling the problem of collinearity in high dimension and enjoys the oracle property. Moreover, we show that AdaGril estimator achieves a Sparsity Inequality, i.e., a bound in terms of the number of non-zero components of the “true” regression coefficient. This bound is obtained under a similar weak Restricted Eigenvalue (RE) condition used for Lasso. Simulations studies show that some particular cases of AdaGril outperform its competitors.     

A comparison of various methods for multivariate regression with highly collinear variables

Regression tends to give very unstable and unreliable regression weights when predictors are highly collinear. Several methods have been proposed to counter this problem. A subset of these do so by finding components that summarize the information in the predictors and the criterion variables. The present paper compares six such methods (two of which are almost completely new) to ordinary regression: Partial least Squares (PLS), Principal Component regression (PCR), Principle covariates regression, reduced rank regression, and two variants of what is called power regression. The comparison is mainly done by means of a series of simulation studies, in which data are constructed in various ways, with different degrees of collinearity and noise, and the methods are compared in terms of their capability of recovering the population regression weights, as well as their prediction quality for the complete population. It turns out that recovery of regression weights in situations with collinearity is often very poor by all methods, unless the regression weights lie in the subspace spanning the first few principal components of the predictor variables. In those cases, typically PLS and PCR give the best recoveries of regression weights. The picture is inconclusive, however, because, especially in the study with more real life like simulated data, PLS and PCR gave the poorest recoveries of regression weights in conditions with relatively low noise and collinearity. It seems that PLS and PCR are particularly indicated in cases with much collinearity, whereas in other cases it is better to use ordinary regression. As far as prediction is concerned: Prediction suffers far less from collinearity than recovery of the regression weights.     

VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component selection becomes that of selecting the groups of coefficients in the expansion. We apply the adaptive group Lasso to select nonzero components, using the group Lasso to obtain an initial estimator and reduce the dimension of the problem. We give conditions under which the group Lasso selects a model whose number of components is comparable with the underlying model, and the adaptive group Lasso selects the nonzero components correctly with probability approaching one as the sample size increases and achieves the optimal rate of convergence. The results of Monte Carlo experiments show that the adaptive group Lasso procedure works well with samples of moderate size. A data example is used to illustrate the application of the proposed method.     

Linear and nonlinear causality tests in an LSTAR model: wavelet decomposition in a nonlinear environment

In this paper, we use simulated data to investigate the power of different causality tests in a two-dimensional vector autoregressive (VAR) model. The data are presented in a nonlinear environment that is modelled using a logistic smooth transition autoregressive function. We use both linear and nonlinear causality tests to investigate the unidirection causality relationship and compare the power of these tests. The linear test is the commonly used Granger causality F test. The nonlinear test is a non-parametric test based on Baek and Brock [A general test for non-linear Granger causality: Bivariate model. Tech. Rep., Iowa State University and University of Wisconsin, Madison, WI, 1992] and Hiemstra and Jones [Testing for linear and non-linear Granger causality in the stock price–volume relation, J. Finance 49(5) (1994), pp. 1639–1664]. When implementing the nonlinear test, we use separately the original data, the linear VAR filtered residuals, and the wavelet decomposed series based on wavelet multiresolution analysis. The VAR filtered residuals and the wavelet decomposition series are used to extract the nonlinear structure of the original data. The simulation results show that the non-parametric test based on the wavelet decomposition series (which is a model-free approach) has the highest power to explore the causality relationship in nonlinear models.     

Logistic回归的双层变量选择研究

变量选择是统计建模的重要环节,选择合适的变量可以建立结构简单、预测精准的稳健模型。本文在logistic回归下提出了新的双层变量选择惩罚方法——adaptive Sparse Group Lasso(adSGL),其独特之处在于基于变量的分组结构作筛选,实现了组内和组间双层选择。该方法的优点是对各单个系数和组系数采取不同程度的惩罚,避免了过度惩罚大系数,从而提高了模型的估计和预测精度。求解的难点是惩罚似然函数不是严格凸的,因此本文基于组坐标下降法求解模型,并建立了调整参数的选取准则。模拟分析表明,对比现有代表性方法Sparse Group Lasso、Group Lasso及Lasso,adSGL法不仅提高了双层选择精度,而且降低了模型误差。最后本文将adSGL法应用到信用卡信用评分研究,对比logistic回归,它具有更高的分类精度和稳健性。     

Using Liu-Type Estimator to Combat Collinearity

Abstract

Linear regression model and least squares method are widely used in many fields of natural and social sciences. In the presence of collinearity, the least squares estimator is unstable and often gives misleading information. Ridge regression is the most common method to overcome this problem. We find that when there exists severe collinearity, the shrinkage parameter selected by existing methods for ridge regression may not fully address the ill conditioning problem. To solve this problem, we propose a new two-parameter estimator. We show using both theoretic results and simulation that our new estimator has two advantages over ridge regression. First, our estimator has less mean squared error (MSE). Second, our estimator can fully address the ill conditioning problem. A numerical example from literature is used to illustrate the results.     

Bayesian variable selection and estimation in maximum entropy quantile regression

Quantile regression has gained increasing popularity as it provides richer information than the regular mean regression, and variable selection plays an important role in the quantile regression model building process, as it improves the prediction accuracy by choosing an appropriate subset of regression predictors. Unlike the traditional quantile regression, we consider the quantile as an unknown parameter and estimate it jointly with other regression coefficients. In particular, we adopt the Bayesian adaptive Lasso for the maximum entropy quantile regression. A flat prior is chosen for the quantile parameter due to the lack of information on it. The proposed method not only addresses the problem about which quantile would be the most probable one among all the candidates, but also reflects the inner relationship of the data through the estimated quantile. We develop an efficient Gibbs sampler algorithm and show that the performance of our proposed method is superior than the Bayesian adaptive Lasso and Bayesian Lasso through simulation studies and a real data analysis.     

中国与美国加拿大小麦贸易中的价格关系

 如何理解和把握小麦国际贸易中的价格决定与影响机制一直以来都是学术界和政府决策部门关注的重要领域。本研究引入并发展了基于关联积分的蒙特卡洛非线性因果关系检验模型，这是一种不需要以假定的线性关系或者预设的函数关系为前提，并同时可以进行因果关系的时效性和影响强度检验的非参数估计模型。本文首次对模型精度e的选择进行了系统讨论和发展，并提出非线性因果影响强度的概念。利用该扩展模型，我们对1996-2008年中美与中加之间的小麦价格进行实证检验，结果显示了双向因果关系，美国和加拿大对我国小麦价格具有显著影响，同时我国小麦价格也对其产生反向调节影响，但在时效和强度上存在较大差异。在理论解释基础上，本文提出了相关政策建议。     

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。     

The small sample properties of the restricted principal component regression estimator in linear regression model

In regression analysis, to deal with the problem of multicollinearity, the restricted principal components regression estimator is proposed. In this paper, we compared the restricted principal components regression estimator, the principal components regression estimator, and the ordinary least-squares estimator with each other under the Pitman's closeness criterion. We showed that the restricted principal components regression estimator is always superior to the principal components regression estimator, under certain conditions the restricted principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion and under certain conditions the principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion.