判别环上矩阵可对角化的一种方法

本文得到了判别不含零因子环上矩阵可对角化的一种方法,并给出了一个四元数体上矩阵用这种方法来判定的例子。     

曲线箱梁有限条法计算程序

采用自然坐标系统,根据圆锥壳应变—位移关系,导得简支曲线条元的应变矩阵、单元刚度矩阵及其相容荷载列阵,在IBM—PC微机上编制了计算机程序,通过曲线箱梁实例计算表明,当加大半径时,曲条法与笔者另行编制的高阶直条法结果吻合良好;当缩小半径时,曲线箱梁的内力变化规律与实际相符,证实了程序的正确性。     

矩阵方程AX-XB=C

本文利用矩阵的 Frobenius 标准形讨论了矩阵方程 AX-XB=C 的解的情况,特别给出了该方程有解时的递推解法,同时给出了该方程有唯一解的充要条件的另一个证明,且证明过程不用克罗内克尔乘法     

THE CONSTRUCTION OF EQUILEVERAGE DESIGNS FOR MULTIPLE LINEAR REGRESSION

The hat matrix is widely used as a diagnostic tool in linear regression because it contains the leverages which the independent variables exert on the fitted values. In some experiments, cases with high leverage may be avoided by judicious choice of design for the independent variables. A variety of methods for constructing equileverage designs for linear regression are discussed. Such designs remove one of the factors, namely large leverage points, which can lead to nonrobust estimators and tests. In addition, a method is given for combining equileverage designs to test for lack of fit of the linear model.     

基于关系网络的新型学习控制

设计了一种不同于传统智能算法如自适应控制与模糊控制等的智能控制算法,该算法基于目标输入关系网络, 借鉴强化学习的思想,采用输出试探与评价进行学习,是一种模型无关的控制算法,该算法可以与随机优化算法结合,通 过实验,验证了其在控制过程中有效性,并通过与遗传算法结合,验证了与遗传算法相结合的该智能算法的控制效果。     

国有银行股份制改造中的组织结构调整

组织结构的有效设计是企业高效运行的重要保证,现代企业管理模式基本上沿着从“金字塔”式的垂直管理向扁平化矩阵式管理方向演进,企业的中间管理环节缩短,管理效能进一步提高。目前,我国各商业银行都在紧锣密鼓抓紧上市,但其中一大障碍就是商业银行的组织结构不合理,本文从国有商业银行组织结构现状及弊端出发,分析了国外商业银行主要组织结构模式,对国有商业银行组织结构再造进行了探讨。     

Maximum likelihood estimation of the linearly structured correlation matrix by a Jacobi-type iterative scheme

Mukherjee and Maiti [Q-procedure for solving likelihood equations in the analysis of covariance structures, Comput. Statist. Quart. 2 (1988), pp. 105–128] proposed an iterative scheme to derive the maximum likelihood estimates of the parameters involved in the population covariance matrix when it is linearly structured. The present investigation provides a Jacobi-type of iterative scheme, MSIII, when the underlying correlation matrix is linearly structured. Such scheme is shown to be quite competent and efficient compared to the prevalent Fisher-scoring (FS) and the Newton–Raphson iterative scheme (NR). An illustrative example is provided for a numerical comparison of the iterates of MSIII, FS and NR choosing the Toeplitz matrix as the population correlation matrix. Numerical behaviour of such schemes is studied in the context of ‘bad’ initial try-out vectors. Additionally a simulation experiment is performed to judge the superiority of MSIII over FS.     

Empirical distribution function under heteroscedasticity

Neglecting heteroscedasticity of error terms may imply the wrong identification of a regression model (see appendix). Employment of (heteroscedasticity resistent) White's estimator of covariance matrix of estimates of regression coefficients may lead to the correct decision about the significance of individual explanatory variables under heteroscedasticity. However, White's estimator of covariance matrix was established for least squares (LS)-regression analysis (in the case when error terms are normally distributed, LS- and maximum likelihood (ML)-analysis coincide and hence then White's estimate of covariance matrix is available for ML-regression analysis, tool). To establish White's-type estimate for another estimator of regression coefficients requires Bahadur representation of the estimator in question, under heteroscedasticity of error terms. The derivation of Bahadur representation for other (robust) estimators requires some tools. As the key too proved to be a tight approximation of the empirical distribution function (d.f.) of residuals by the theoretical d.f. of the error terms of the regression model. We need the approximation to be uniform in the argument of d.f. as well as in regression coefficients. The present paper offers this approximation for the situation when the error terms are heteroscedastic.     

Design effect of randomized systematic sampling

In statistical practice, systematic sampling (SYS) is used in many modifications due to its simple handling. In addition, SYS may provide efficiency gains if it is well adjusted to the structure of the population under study. However, if SYS is based on an inappropriate picture of the population a high decrease of efficiency, i.e. a high increase in variance may result by changing from simple random sampling to SYS. In the context of two-stage designs SYS so far seems often in use for subsampling within the primary units. As an alternative to this practice, we propose to randomize the order of the primary units, then to select systematically a number of primary units and, thereafter, to draw secondary units by simple random sampling without replacement within the primary units selected. This procedure is more efficient than simple random sampling with replacement from the whole population of all secondary units, i.e. the variance of an adequate estimator for a total is never increased by changing from simple random sampling to randomized SYS whatever be the values associated by a characteristic with the secondary units, while there are values for which the variance decreases for the change mentioned. This result should hold generally, even if our proof, so far, is not complete for general sample sizes.     

中国省际经济差距来源分析

在利用索洛模型对中国省区1985—2009年经济增长进行分解的基础上,结合空间标准差指标并采用基于VAR模型的脉冲响应函数分析了中国省际经济差距状况及来源。研究发现:总的来看,中国省区劳均产出与要素投入均呈现空间σ趋异倾向,而全要素生产率则在呈现空间σ收敛后趋于稳定。进一步利用VAR模型及脉冲响应函数分析发现,在较长时期内,要素投入总体上扩大了中国省际经济差距,而全要素生产率则有助于缩小省际经济差距,这主要是由要素投入的经济拉动滞后效应和技术的扩散效应所致。