基于偏最小二乘方法的信用评分模型

为了克服信用评分模型中自变量存在多重共线性的问题,文章引入了偏最小二乘思想,即采用限制预测值的偏最小二乘回归和偏最小二乘Logistic回归来创建信用评分模型。偏最小二乘法可以同时解释因变量和自变量的变异,在实际运用中更加符合信用评分模型的特点。实证研究的结果表明,利用这两种偏最小二乘模型创建的信用评分模型具有很好的准确性和稳定性。     

基于双重筛选的多因变量偏最小二乘逐步回归方法

偏最小二乘回归分析中的一个重要问题是变量选择,文章的主要目的是给出一种改进的多元数据分析方法-基于双重筛选的多因变量偏最小二乘逐步回归方法。双重筛选方法既能按自变量对因变量的关系进行分组,又能使每个自变量对各组因变量的作用反映出来。因此基于双重筛选的多因变量偏最小二乘回归方法能很好地处理这类问题,并得到好的结果。     

谈直线回归方程的应用条件

当前，随着统计事业的发展，最小二乘法已成为统计分析工作中的最基本方法之一。不论是时间数列的动态分析、还是横截面的静态分析，最小二乘法都发挥着极大的作用。一、最小二乘法直线方程的剖析对于一个数列，如果用最小二乘法配合直线模型，首先要求其自变量是一个非随机的变量。例如：研究某一社会经济现象随时间的变化规律，时间就是一个非随机变量。但是如果研究身高与体重、收入与支出等现象时，被研究的两个变量都是随机变量。在后一种情况下利用最小二乘法时，应假定某一作为自变量的变量是非随机变量，然后再做直线的回归。由于这…     

基于一元线性回归模型异方差对加权最小二乘法的考察

作为普通最小二乘法的改进,加权最小二乘法用于存在异方差问题的线性回归模型的参数估计。文章通过对加权最小二乘估计量、加权最小二乘变换的分析,并结合实际例证研究发现,加权最小二乘法在应用中存在一些不足之处,因而当发现模型存在异方差时使用加权最小二乘法是存在风险的。     

成本预测系统中的自变量约简方法

文章针对成本预测系统中自变量众多且相互关系错综复杂的特点,提出用模糊粗糙集方法对成本预测系统中的自变量进行约简。在模糊粗糙集方法的框架下,给出了模糊等价关系、不可分辨关系和相对约简的定义,构建了基于模糊粗糙集的成本预测系统自变量约简模型。并且针对实际的成本预测系统一般是混合变量数据系统的情形,对广义差别矩阵的定义进行了改进,并以此设计了相应的启发式约简算法。实例分析结果表明,文中所提的方法较之传统的灰色关联系数法、主成分分析法和偏最小二乘回归法,自变量约简效果最佳,所提方法是科学和有效的。     

分位数回归的思想与简单应用

与普通最小二乘法相比,分位数回归能够更充分反映自变量对不同部分因变量的分布产生不同的影响,有着十分广泛的应用。本文对分位数回归的思想做了一个简单的介绍,并将其方法应用于恩格尔定律中,比较分析了异方差和同方差下分位数回归与普通最小二乘法的优劣。     

基于正态模糊数回归分析模型的构建与评价

文章采用模糊最小二乘法,求解自变量为精确数、因变量和回归系数均是正态模糊数的一元线性模糊回归模型,证明所求得的模糊估计量具有的统计性质:线性性与无偏性.给出模糊回归模型的残差、残差平方和及拟合优度公式.将方法应用于一个实际问题,并与经典回归分析进行比较,验证了该参数估计方法的合理性与有效性.     

基于SSA-MGF的偏最小二乘回归预测模型

本文利用奇异谱分析和均生函数方法,对原始序列重构延拓作为自变量,原始序列作为因变量,建立偏最小二乘回归预测模型,并与主成分最小二乘回归预测模型比较分析.实例结果表明,该方法具有预测精度高、稳定好的特点.     

关于统计学教学中"最小二乘法"的讲授

文章着重从动态数列分析、回归分析的有关模型参数估计以及相关分析中相关系数公式的推导中阐明“最小二乘法”的应用和讲授 ,并强调“最小二乘法”本身并不是一种模型预测方法 ,而是一种模型参数估计方法 ,并在推导皮尔逊的乘积动差法相关系数中得到应用     

线性化最小二乘法的理论分析

在处理非线性回归中的可线性化回归问题时,最小二乘法给了我们很大的方便.但是人们在享有其优点的同时,忽视了其结果准确性问题.文章从理论上给出了线性最小二乘法结果准确性的证明并提出了解决方法.     

A fuzzy robust regression approach applied to bedload transport data

Fuzzy least-square regression can be very sensitive to unusual data (e.g., outliers). In this article, we describe how to fit an alternative robust-regression estimator in fuzzy environment, which attempts to identify and ignore unusual data. The proposed approach concerns classical robust regression and estimation methods that are insensitive to outliers. In this regard, based on the least trimmed square estimation method, an estimation procedure is proposed for determining the coefficients of the fuzzy regression model for crisp input-fuzzy output data. The investigated fuzzy regression model is applied to bedload transport data forecasting suspended load by discharge based on a real world data. The accuracy of the proposed method is compared with the well-known fuzzy least-square regression model. The comparison results reveal that the fuzzy robust regression model performs better than the other models in suspended load estimation for the particular dataset. This comparison is done based on a similarity measure between fuzzy sets. The proposed model is general and can be used for modeling natural phenomena whose available observations are reported as imprecise rather than crisp.     

地理距离、方言文化与劳动力空间流动

本文基于百度迁徙大数据研究中国劳动力的空间流动，系统考察地理和文化对劳动力流动的影响。通过构造流动机会比率，基于引力模型和普通最小二乘法的研究表明地理距离和方言距离阻碍劳动力流动。在空间距离上，劳动力偏好邻近城市，地理距离每增加1%，劳动力的流动机会比率降低约0.6%。在空间位置上，劳动力倾向于在方言文化相近地域范围流动，方言距离每增加1%，劳动力的流动机会比率下降2%左右。通过构造两地年均降水量差距和小麦种植适宜度差距作为方言距离的工具变量，以两阶段最小二乘法估计缓解内生性问题，估计显示结论稳健。考虑普通话因素后方言距离的抑制影响依然稳健，但目的地的高普通话普及率显著发挥促进劳动力流动的引力作用。最后，本文得出持续推广普通话、加强交通建设和深化中等教育的政策建议。     

再议普通最小二乘法下回归系数的性质

文章从个体的角度探讨最小二乘法下的估计系数的形成过程,得出一元回归中的回归系数是各个数据点上的回归系数以Epanechnikov核函数进行加权形式的。并在此基础上,推广到多元线性回归,多元线性回归的估计系数本质上为一种参数结构,它是以自变量的协方差矩阵为联系纽带,将回归系数分解为偏回归系数,将两个系数结合起来澄清目前计量经济学和统计学的一些问题。     

Parametric Estimator of Linear Model with Interval-Censored Data

In this article, we consider the estimation of regression parameters in linear model in the presence of interval-censored data. When the response variable is interval-censored, the traditional methods can not be used to estimate the parameters directly. In this article, unbiased transformation is carried out and a new random variable which has the same expectation as the function of the response variable is established. With the regression analysis for the constructed statistic we conclude the estimator by least square method.     

Multivariate regression models for discrete and continuous repeated measurements

A general class of multivariate regression models is considered for repeated measurements with discrete and continuous outcome variables. The proposed model is based on the seemingly unrelated regression model (Zellner, 1962) and an extension of the model of Park and Woolson(1992). The regression parameters of the model are consistently estimated using the two-stage least squares method. When the out come variables are multivariate normal, the two-stage estimator reduces to Zellner’s two-stage estimator. As a special case, we consider the marginal distribution described by Liang and Zeger (1986). Under this this distributional assumption, we show that the two-stage estimator has similar asymptotic properties and comparable small sample properties to Liang and Zeger's estimator. Since the proposed approach is based on the least squares method, however, any distributional assumption is not required for variables outcome variables. As a result, the proposed estimator is more robust to the marginal distribution of outcomes.     

Iterative regularisation in nonparametric instrumental regression

This paper considers the nonparametric regression model with an additive error that is correlated with the explanatory variables. Motivated by empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. However, the estimation of a nonparametric regression function by instrumental variables is an ill-posed linear inverse problem with an unknown but estimable operator. We provide a new estimator of the regression function that is based on projection onto finite dimensional spaces and that includes an iterative regularisation method (the Landweber–Fridman method). The optimal number of iterations and the convergence of the mean square error of the resulting estimator are derived under both strong and weak source conditions. A Monte Carlo exercise shows the impact of some parameters on the estimator and concludes on the reasonable finite sample performance of the new estimator.     

On small sample properties of the mixed regression predictor under misspecification

This paper relaxes the Mittelhammer's (1981) assumption that the value of the true variance is known in the mixed regression model and examines the small sample, properties of the feasible mixed regression predictor under misspecification. The paper shows that the feasible mixed regression predictor is not always superior to the ordinary least squares predictor in terms of the weak mean square error when there exist omitted variables in the model. Further it shows that misspecificstion works favorably for the ordinary least squares predictor.     

模糊数据的回归模型结构分析

本文在给出对称三角模糊数样本基础上,提出模糊数据回归分析模型的一般结构。在使用线性规划LP方法进行模糊回归系数估计时,根据模糊集合的择近原则,给出了利用样本平均贴近度评价模型拟合效果的一个准则。通过实例计算,比较了模糊样本回归模型未知参数估计的FLP方法和FLS 方法。     

The effects of the proxy information on the iterative Stein-rule estimator of the disturbance variance

In a regression model with proxy variables, we consider the iterative estimator of the disturbance variance to obtain more precise estimates. In the formula of the estimator of the disturbance variance, the estimator is obtained by using Stein-rule (SR) estimator instead of OLS (ordinary least squares) estimator is called Iterative estimator of the disturbance variance. It is shown that, in a regression model with proxy variables the mean square error (MSE) of the iterative estimator of the disturbance variance is greater than the MSE of the disturbance variance related to the OLS estimator under certain conditions.     

Dropping variables versus use of proxy variables in linear regression

In this paper we investigate under which conditions it is preferable to use proxies or to omit variables from the linear regression model with respect to the matrix mean square error criterion. Furthermore, some attention is paid to the admissibility of the proxies-based least squares estimator.