矩阵的广义逆与线性方程组的反问题

本文讨论了矩阵的广义逆的若干性质，并利用一类特殊的广义逆──左逆，给出了求解线性方程组的反问题和一般性方法．     

几族全着色临界图

本文引进全着色矩阵的概念,每个全着色矩阵确定一个简单图及其一全着色。若图G的全色数为k,G的任一真子图的全色数均小于k,称G为k-全着色临界图。对任意奇数r>3,我们给出若干阶数最小的非平凡r~-全着色临界图。     

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.     

问卷分割设计的模拟研究——小域估计的一种应用

针对长问卷存在无回答率和回答负担,从而导致统计调查精度降低的问题,采用问卷分割法解决该问题,并且通过小域估计的方法进行参数估计。模拟研究表明,利用小域估计方法对分割问卷进行参数估计显然优于用多重插补法进行参数估计。研究结果表明,运用小域估计方法对分割问卷进行参数估计,能显著提高统计调查的精度。     

广义次正定复矩阵及其性质

继续研究决正定矩阵的理论，定义了复数域上的广义次正定矩阵，讨论了它的一系列性质．     

On the skew-normal calibration model

In this article, we present the EM-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conducted for evaluating the performance of the calibration estimator with interpolation and extrapolation situations. As one application in a real data set, we fitted the model studied in a dimensional measurement method used for calculating the testicular volume through a caliper and its calibration by using ultrasonography as the standard method. By applying this methodology, we do not need to transform the variables to have symmetrical errors. Another interesting aspect of the approach is that the developed transformation to make the information matrix nonsingular, when the skewness parameter is near zero, leaves the parameter of interest unchanged. Model fitting is implemented and the best choice between the usual calibration model and the model proposed in this article was evaluated by developing the Akaike information criterion, Schwarz’s Bayesian information criterion and Hannan–Quinn criterion.     

On optimal linear equivariant estimation under progressive censoring

We consider best linear equivariant estimation in a particular location-scale family based on several progressively type II censored samples. The censoring schemes that minimize the mean squared error matrix of the estimators with respect to the Löwner ordering are obtained. Uniqueness of the schemes, which minimize the smallest and the largest eigenvalue of the matrix is shown under some condition.