论文检索

多元问题中的广义贝叶斯估计量AI 解读

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：SHAZAMAI 解读

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AI 解读

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AI 解读

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AI 解读

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AI 解读

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AI 解读

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AI 解读

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.

摘要暂缺

多重共线性情形下的定向岭回归技术AI 解读

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AI 解读

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AI 解读

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AI 解读

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.

多元回归变量选择的停止规则AI 解读

Stepwise regression is a member of a class of statistical methods which may be called opportunistic. The statistician is naturally concerned that an artifact should not be reported so he needs a stopping rule that is geared to the way in which variables are selected. A sampled permutation test is outlined which offers such a stopping rule for forward stepping.