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实例回归分析
Simple Linear Regression Multiple Linear Regression Regression Diagnostics: Detection of Model Violations Qualitative Variables as Predictors Transformation of Variables Weighted Least Squares The Problem of Correlated Errors Analysis of Collinear Data Biased Estimation of Regression Coefficients Variable Selection Procedures Logistic Regression Appendix References Index.
岭回归估计的极小极大性质
The technique of ridge regression, first proposed by Hoerl and Kennard, has become a popular tool for data analysts faced with a high degree of multicollinearity in their data. By using a ridge estimator, one hopes to both stabilize one's estimates (lower the condition number of the design matrix) and improve upon the squared error loss of the least squares estimator. Recently, much attention has been focused on the latter objective. Building on the work of Stein and others,…
一类岭回归估计量的频率学派分析
We discuss ridge regression estimators as a class, showing how six recently proposed estimators can thus be viewed, and give reasons for preferring one of these (empirical Bayes maximum likelihood estimator) to the other five. Results are based on analysis rather than simulations and on a frequentist rather than Bayesian viewpoint.
一类岭回归估计量的频率学派分析
We discuss ridge regression estimators as a class, showing how six recently proposed estimators can thus be viewed, and give reasons for preferring one of these (empirical Bayes maximum likelihood estimator) to the other five. Results are based on analysis rather than simulations and on a frequentist rather than Bayesian viewpoint.
基于离散最大惩罚似然准则的非参数密度估计
A nonparametric probability density estimator is proposed that is optimal with respect to a discretized form of a continuous penalized-likelihood criterion functional. Approximation results relating the discrete estimator to the estimate obtained by solving the corresponding infinite-dimensional problem are presented. The discrete estimator is shown to be consistent. The numerical implementation of this discrete estimator is outlined and examples displayed. A simulation…
对若干岭回归方法的批评
Ridge estimates seem motivated by a belief that least squares estimates tend to be too large, particularly when there is multicollinearity. The ridge solution is to supplement the data by stochastically shrinking the estimates toward zero. Although flexibility is provided by the abstention from exact exclusion restrictions, ridge regression retains many weaknesses of similarly motivated procedures : a neglect of the basic fact that linear transformations should not change…
惩罚似然密度估计与峰值识别：散射及陨石数据示例
The (maximum) penalized-likelihood method of probability density estimation and bump-hunting is improved and exemplified by applications to scattering and chondrite data. We show how the hyperparameter in the method can be satisfactorily estimated by using statistics of goodness of fit. A Fourier expansion is found to be usually more expeditious than a Hermite expansion but a compromise is useful. The best fit to the scattering data has 13 bumps, all of which are evaluated…
自适应多元岭回归
A multivariate version of the Hoerl-Kennard ridge regression rule is introduced. The choice from among a large class of possible generalizations is guided by Bayesian considerations; the result is implicitly in the work of Lindley and Smith although not actually derived there. The proposed rule, in a variety of equivalent forms is discussed and the choice of its ridge matrix considered. As well, adaptive multivariate ridge rules and closely related empirical Bayes procedures…
正态离散矩阵的贝叶斯推断及其在随机多元回归中的应用
Summary This paper discusses Bayesian inference procedures for a normal dispersion matrix. Structural information for the prior mean of the dispersion matrix is incorporated into the analysis through a Normal-Wishart prior distribution. Many of the resulting Bayes estimates are invariant, consistent and asymptotically efficient. Using this procedure, a coherent Bayesian argument for stochastic multiple regression analysis is developed, where dependent and independent…
一类收缩估计量
Summary In this paper we define a class of shrinkage estimators, all of whose members have a mean square error matrix which is less than that of the ordinary least squares estimator by a positive semidefinite matrix if (β-b *)T X T X (β-b *) ≤ σ2. The ridge regression, principal component and minimum conditional mean square error estimators are members of this class.
极小极大自适应广义岭回归估计量
We consider the problem of estimating the vector of regression coefficients of a linear model using generalized ridge regression estimators where the ridge constant is chosen on the basis of the data. For general quadratic loss we produce such estimators whose risk function dominates that of the least squares procedure provided the number of regressors is at least three. We study the problem by the usual reduction to estimating the mean vector of a multivariate normal…
多元问题中的广义贝叶斯估计量
Several problems involving multivariate generalized Bayes estimators are investigated. First, a characterization of admissible estimators as generalized Bayes estimators is developed for certain multivariate exponential families and quadratic loss. The problem of verifying whether or not an estimator is generalized Bayes is also considered. Next, an important class of estimators for a multivariate normal mean is considered. (The class includes many minimax, empirical Bayes,…
计量经济模型的通用计算程序：SHAZAM
to prepare and allow a large number of options. The program can be run in batch mode or interactively at a computer terminal. Computer core storage is dynamically allocated so that large problems are only limited by the size of the machine. SHAZAM is designed to grow so that new algorithms and procedures can easily be added by any programmer familiar with the internal structure of the program. Features of SHAZAM include ordinary least squares, two-stage least squares,…
回归中的有偏估计：基于均方误差的评价
A mean squared error criterion is used to compare five estimators of the coefficients in a linear regression model: least squares, principal components, ridge regression, latent root, and a shrunken estimator. Each of the biased estimators is shown to offer improvement in mean squared error over least squares for a wide range of choices of the parameters of the model. The results of a simulation involving all five estimators indicate that the principal components and latent…
多重判别分析中变量选择的同时检验程序
The purpose of the procedures proposed in this paper is to provide information about the relative importance of variable subsets in the analysis of multivariate data. In multiple discriminant analysis the procedures isolate subsets of variables which provide essentially as much separation among the groups in each subset of groups as the original set of variables. Each procedure is a simultaneous test procedure in that the type I probability error rate for the family of…
多重判别分析中变量选择的同时推断程序
The purpose of the procedures proposed in this paper is to provide information about the relative importance of variable subsets in the analysis of multivariate data. In multiple discriminant analysis the procedures isolate subsets of variables which provide essentially as much separation among the groups in each subset of groups as the original set of variables. Each procedure is a simultaneous test procedure in that the type I probability error rate for the family of…
多元回归中的变量选择：同时检验程序的应用
Summary Simultaneous procedures for variable selection in multiple linear regression have recently been given by Aitkin. One of these procedures, proposed for the case when the regression equation is to be used for descriptive purposes, is an application of each of a number of simultaneous procedures concerned with the multivariate general linear model and given by Gabriel with applications in the manova context. The applications of Gabriel's procedures to multivariate…
普通最小二乘替代方法的模拟研究
Estimated regression coefficients and errors in these estimates are computed for 160 artificial data sets drawn from 160 normal linear models structured according to factorial designs. Ordinary multiple regression (OREG) is compared with 56 alternatives which pull some or all estimated regression coefficients some or all the way to zero. Substantial improvements over OREG are exhibited when collinearity effects are present, noncentrality in the original model is small, and…
新岭回归方法在贝尔系统规模经济研究中的应用
We suggest a new horizontal scaling for the ridge trace, some new techniques for monitoring ridge solutions including an index of stability of relative magnitudes (ISRM) and numerical largeness of more significant (NLMS) regression coefficients. A method of curtailing the tending of ridge regression coefficients toward zero is also presented. Two examples illustrate these methods and estimate Bell System's scale economies to be large.
多重共线性情形下的定向岭回归技术
In the presence of multicollinearity ridge regression techniques result in estimated coefficients that are biased but have a smaller variance than ordinary least squares (OLS) estimators and may, therefore, have a smaller mean square error. The directed ridge estimator (DRE) suggested here alters only diagonal elements corresponding to relatively small eigenvalues. The advantage of our method is that the resulting estimates may be less biased than in other ridge regression…
惩罚函数法下概率密度的非参数最大似然估计
Tne maximum likelihood estimate of a probability density function based on a random sample does not exist in the nonparametric case. For this reason and others based on heuristic Bayesian considerations Good and Gaskins suggested adding a penalty term to the likelihood. They proposed two penalty terms; however they did not establish existence or uniqueness of their maximum penalized likelihood estimates. Good and Gaskins also suggested an alternate approach for calculating…
若干岭型估计量的蒙特卡洛评估
Consider the standard linear model . Ridge regression, as viewed here, defines a class of estimators of indexed by a scalar parameter k. Two analytic methods of specifying k are proposed and evaluated in terms of mean square error by Monte Carlo simulations. With three explanatory variables and determined by the largest eigenvalue of the correlation matrix, least squares is dominated by these estimators in all cases investigated; however, mixed results are obtained with…
均方误差的推广及其在岭回归中的应用
Summary Hoerl and Kennard (1970) have proposed a method of estimation for multiple regression problems which involves adding small positive quantities to the diagonal of XT X. They use a type of mean square error to justify the procedure. This paper considers some generalizations of mean square error and provides a stronger defence of the method.