Matrix mean square error comparisons based on a certain covariance structure

For two given estimators of a parameter vector the covariance structure of their difference is used to compare them in terms of their mean square error matrices. The results obtained are applied to the covariance adjustment technique and regression     

特征值与特征向量相关问题的研究

特征值与特征向量是代数研究的中心问题之一,是两个密切相关的概念.在理论和实际应用中,特征值与特征向量都有举足轻重的地位.本文主要是对矩阵特征值与特征向量进行讨论,给出关于特征值与特征向量的相关命题.并对有关特征值与特征向量的题型做了解析以及解题的错误做出相应分析.     

《黑客帝国》与"中枢神经系统的延伸"

从中枢神经系统延伸的由来、有关“真实性”、实现和未来四个方面论述在电影《黑客帝国》中涉及的数字技术对人类未来社会将可能产生的影响。沃卓斯基兄弟通过电影媒介形式的《黑客帝国》传递了关于未来的讯息:人们正在被深深地卷入一个数字化的世界,人们的选择将决定自己未来的生存方式。     

一类复矩阵的特征性质

本文证明了满足特征条件AA=αA~2的矩阵是A=αA且│α│=1。     

层次分析法在企业筹资决策中的应用研究

将运筹学中的层次分析法应用于企业的筹资决策中,可以减少企业筹资决策的盲目性。本文在建立了筹资决策的层次分析模型的基础上,进行了实证分析并指出了应用此方法应注意的问题。     

The robustness and optimality of response surface designs

Recent work on extended optimality criteria for robust designs is applied to response surface problems. Methods of calculation are described and the criteria illustrated with several examples. The extended criteria discriminate among designs equivalent by other criteria.     

基于粗糙集与主成分分析的属性约简的启发式算法研究

信息系统的属性约简反映了一个决策表的本质信息,为信息系统的数据挖掘奠定的基础。生成一个决策表的所有约简或计算出最佳(定义为属性数目最少)的约简都是NP难问题。目前已有的基于粗糙集的属性约简算法由于计算复杂较高,而不适用大规模数据。本文探讨了一种基于区分矩阵和主成分分析的算法,该算法利用属性在区分矩阵中频率及属性贡献率做为启发规则,寻找最小约简,并在海关通关风险评估系统中得到良好的应用。     

An Application of Matrix Power Series to Linear Models

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.     

A Note on Wald's Type Chi-squared Tests of Fit

The Wald's method for constructing chi-squared tests of fit has been formulated more accurately. It is shown that Wald's type statistics will follow the central chi-squared distribution if and only if the limit covariance matrix of standardized frequencies will not depend on unknown parameters. Several examples that illustrate this important fact are presented. In particular, it is shown that the goodness-of-fit statistic developed by Moore and Stubblebine does not follow the chi-squared limit distribution, and, hence, cannot be used for testing multivariate normality.