基于泛岭估计对岭估计过度压缩的改进方法

岭估计是解决多元线性回归多重共线性问题的有效方法,是有偏的压缩估计。与普通最小二乘估计相比,岭估计可以降低参数估计的均方误差,但是却增大残差平方和,拟合效果变差。本文提出一种基于泛岭估计对岭估计过度压缩的改进方法,可以改进岭估计的拟合效果,减小岭估计残差平方和的增加幅度。     

Comparisons among some estimators in misspecified linear models with multicollinearity

In this paper we deal with comparisons among several estimators available in situations of multicollinearity (e.g., the r-k class estimator proposed by Baye and Parker, the ordinary ridge regression (ORR) estimator, the principal components regression (PCR) estimator and also the ordinary least squares (OLS) estimator) for a misspecified linear model where misspecification is due to omission of some relevant explanatory variables. These comparisons are made in terms of the mean square error (mse) of the estimators of regression coefficients as well as of the predictor of the conditional mean of the dependent variable. It is found that under the same conditions as in the true model, the superiority of the r-k class estimator over the ORR, PCR and OLS estimators and those of the ORR and PCR estimators over the OLS estimator remain unchanged in the misspecified model. Only in the case of comparison between the ORR and PCR estimators, no definite conclusion regarding the mse dominance of one over the other in the misspecified model can be drawn.     

Statistical Measures for Least Squares Using the αQβR Algorithm

This paper shows how the output derived from the α Qβ R algorithm can be used to calculate various statistical quantities needed to evaluate linear models. In particular, we show how to calculate standard statistical quantities like the coefficient of determination R², the F-statistics, and the t-statistics. These quantities serve as a measure of how well the model fits the data.     

Extracting robust and physically meaningful pitzer parameters for thermodynamic properties of electrolytes from experimental data. Ridge regression as an aid to the problem of intercorrelation

The Pitzer interaction model for thermodynamic properties of electrolytes is reevaluated in view of available regression techniques for the statistical inference of Pitzer parameters from experimental data. It is concluded that ordinary least squares regression is not generally suited, because of the intrinsic correlations among the various predictor variables in the Pitzer model. The predictor variables all are some function of the concentration of the electrolyte considered. Ridge regression, a mathematically only slightly different procedure designed to overcome the problem of intercorrelations, often yields more robust estimates for the Pitzer parameters. The potential of RR is demonstrated by some examples for the system GaCl₃–HCl. The ridge estimates are expected to be closer to the physically true parameter values.     

基于Logistic回归的主成分估计及实证分析

应用主成分估计方法,对Logistic回归模型进行参数估计,并消除多重共线性影响.首先选取了累计贡献率达到85%以上的6个主成分,对因变量进行主成分估计,然后挑选出冠心病患者发病的主要影响因素,最后得到了因变量(冠心病发病)与6个主要影响因素(血压(sbp)、累计烟草量(tobacco)、低密度脂蛋白胆固醇(ldl)、心脏病家族史(famhist)、型表现(typea)和发病年龄(age))的回归模型.根据结果可知,心脏病家族史是导致心脏病发病最大的一个原因,它是一个不可控因素;在可控因素中,累计烟草量对冠心病发病的影响最大,因此建议患者应该控制烟草摄入量,以保证病情的稳定性.     

基于岭估计的岭马田系统在复共线性数据中的应用

在多变量模式识别领域,变量间经常会存在复共线性,复共线性不仅会影响参数估计的效果,也会使变量的敏感性出现显著异常.马田系统是以马氏距离作为测量尺度的多变量模式识别方法,复共线性会通过马氏距离影响马田系统变量筛选的效果和判别的准确率.基于岭估计提出了一种新的测量尺度—岭马氏距离,利用岭迹法确定岭参数,将其引入马田系统使得马田系统对病态数据具有更好的耐受性.通过案例验证了岭马氏距离可以很好的克服复共线性,并提高马田系统的判别准确率.     

Improved estimation under collinearity and squared error loss

This paper examines the performance of several biased, Stein-like and empirical Bayes estimators for the general linear statistical model under conditions of collinearity. A new criterion for deleting principal components, based on an unbiased estimator of risk, is introduced. Using a squared error measure and Monte Carlo sampling experiments, the resulting estimator's performance is evaluated and compared with other traditional and non-traditional estimators.     

主变量筛选方法

本文利用矩阵的扫描运算，提出一种对高维随机向量X=（x1,x2,…,xp)‘进行降维处理的实用方法-主变量筛选方法，给出了该方法的理论依据、直观解释、算法及数值例子。该方法是不同于主成分分析法的一种降维方法。特别，当变量X多重相关性突出时，本文方法效果显著。     

岭回归在石油钻井工程中的应用

在石油钻井工程中，井壁坍塌的状况即井径的扩大与缩小，与地层中泥页岩的各种理化性质有关，而这些理化参数又存在于一定程度的相关性．本文利用岭回归分析数据进行了分析与处理，建立了井径扩大的数学模型，确定了影响井径的主要理化指标，为倾决井壁坍塌提供了理论依据．     

Analysis of regression in game theory approach

Working with multiple regression analysis a researcher usually wants to know a comparative importance of predictors in the model. However, the analysis can be made difficult because of multicollinearity among regressors, which produces biased coefficients and negative inputs to multiple determination from presum ably useful regressors. To solve this problem we apply a tool from the co‐operative games theory, the Shapley Value imputation. We demonstrate the theoretical and practical advantages of the Shapley Value and show that it provides consistent results in the presence of multicollinearity. Copyright © 2001 John Wiley & Sons, Ltd.