方差矩阵

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

The building rules of GLCM （ the best gray levels and pixels interval） were confirmed by experiment. GLCM texture parameters of 300 wood specimens were calculated and assayed, and then placed into a Competitive Neural Network for classification output. The results are as follows: 1） GLCM parameters Angular Second Moment contrast , correlation , entr

以"角二阶矩"、"对比度"、"相关"、"熵"、"方差"、"逆差矩"作为描述木材纹理的特征参数是合适的。2）在比例为1：1的512×512木材图像情况下，生成灰度共生矩阵的最佳像素间距为4，最佳图像灰度级数为128.3）木材纹理图像灰度共生矩阵的"角二阶矩"、"相关"和"熵"值最大的方向为纹理方向。4）竞争神经网络的分类正确率为88％。

At polymorphic gene locus, the variance components of quantitative trait was described as follows:VA=2βp and VG=p′Xp-G2 in which p=column vector of polymorphic allele frequencies,β=row vector of2,X=［a2ij］i×i matrix,aij=genotype value,and G=population mean.

数量性状相对多态座位的加性方差和遗传方差分别为VA=2βp和VG=p′Xp-G2，其中p′和p分别表示多态等位基因频率的行向量和列向量，X表示以基因型值平方为元素的矩阵，β表示以基因均效平方为元素的行向量，G为群体均数。

It is known theoretically that to the variational problem with weak constraints in cost functional J, its Euler equation can be discreted into difference format, by using matrix theory and difference method of partial differential equation we know that there exists optimal selection of weight factors in the cost functional under the condition of minimal variance between analysis field and ideal field.

从理论上可知，对于目标泛函J带有约束条件的变分问题，将其Euler方程离散成差分形式，利用矩阵理论和偏微分方程的差分方法，则目标泛函的权重因子，在分析场和理想场的最小方差意义下存在最优选取。

The measurement system error model analysis is introduced into power system real time network state analysis as an important part for the first time, which can improve on the state estimation quality and provide the capability to monitor the operation of the measurement system; 2. The theory and algorithm of the on-line estimation and update of measurement noise variance based on the relation between the residual variance and noise variance. The statistic properties of the sample variance are discussed and the relation between the estimation precision and sample size under given confidence level is derived; 3. The theory and algorithm of detection and identification of measurement bias are presented, which is based on the relation between residual mean and noise mean. The statistic properties of sample mean are discussed and the relation between estimation precision and sample size is derived; 4. The Givens orthogonal transformation algorithm is selected to be the essential algorithm of state estimation, the fast orthogonal transformation algorithm with damp factor and the algorithm which can handle the zero injection measurements efficiently are presented; 5. The quantity analysis theory of bad data detectivity and identifibility are presented, which describes the relation between the elements in matrix W〓 and bad data amplitude and can provide the theory base for measurement system design and valuation.

一、首次将量测系统误差模型分析做为一个环节引入电力系统实时网络状态分析中，为EMS系统增加了实时监视系统运行、修正量测系统误差模型的新功能，进一步发挥了实时网络状态分析应用软件的潜力；二、首次提出了应用样本方差在线估计与修正量测系统误差方差的基本理论，讨论了样本方差的统计性质和概率分布，推导出了样本容量、估计精度和置信度之间的关系，给出了在线估计与修正量测系统误差方差的算法；三、首次提出了应用样本均值在线检测与辨识量测偏差的基本理论，讨论了样本均值的统计性质，推导了样本容量、估计精度和置信度之间的基本关系，给出了在线检测与辨识量测偏差的算法；四、在状态估计算法设计中，以Givens变换算法做为基本算法，提出了快速正交变换阻尼因子法和可以有效地处理零注入量测的混合法，并对实时应用中的一些问题进行了讨论；五、提出了不良数据可检测性与可辨识性的定量分析理论，揭示了描述量测系统配置、网络结构与参数的残差灵敏度矩阵中的元素与不良数据的幅值在可检测、可辨识能力上的定量关系，为量测系统配置设计与评价提供了理论基础；六、综合国内外最新研究成果，采用自适应自回归预测技术和稀疏矢量技术，构造了较完善的不良数据检测与辨识算法。

The model this paper deals with is a flow line of two machines. By means of structured stochastic matrix theory and theory of Markov process, an effective algorithm obtaining the variance of end products in a given period is proposed.

讨 论的模型为两级的串行生产线，利用结构随机矩阵理论和马氏过程的协方差结构，给出了在一个给定时间区间内系统生产成品数方差的有效算法。

In chapter 2, the paper considers about applying the regularized method with a variance uniformization constraint to image restoration, therefore we discusses the relation between the variance of the restored image and the singular value of the discrete matrix of the blur operator in detail, and theoretically proves the well-posedness of the regularized method with a variance uniformization constraint.

在第二章中，本文考虑将带一致方差约束的正则化方法应用于图像的恢复，为此详细讨论了恢复图像的方差与模糊算子的离散矩阵的奇异值之间的关系，并从理论上证明了带一致方差约束的正则化方法的适定性。

By the modem time series analysis method, based on the ARMA innovation model, under the linear minimum variance optimal information fusion criterion, three distributed fusion steady-state optimal Kalman filters, predictors and smoothers weighted by matrices, scalars, and diagonal matrices are presented for multisensor systems with correlated input and observation noises, and with correlated observation noises. The Lyapunov equations and formulas of computing local filtering, predicting and smoothing error variances and covariances are given, which are applied to compute optimal weights. The corresponding three distributed fusion Wiener state estimators are also presented.

应用现代时间序列分析方法，基于自回归滑动平均新息模型，在线性最小方差最优信息融合准则下，对于带相关输入噪声和观测噪声和带相关的观测噪声的多传感器系统，提出了按矩阵加权、按标量加权和按对角阵加权的三种分布式融合稳态Kalman滤波器、预报器和平滑器，其中提出了局部滤波、预报和平滑估值误差方差阵和协方差阵的Lyapunov方程和计算公式，它们被用于计算最优加权，也提出了相应的三种分布式融合Wiener状念估值器。

But when there are outliers in the sample, these methods are easily affected by them.

但是当样本数据中包括离群值时，计算结果就会很容易受到这些离群值的影响，这是因为传统的均值向量和协方差矩阵都不是稳健的统计量。

Based on probability theory, a method for describing and calculating the collision probability between rendezvous and docking vehicle and debris is presented, and the method involves quantitatively analyzing the collision probability using quasi maximum instantaneous collision probability and total collision probability. The method calculating the indexes is developed, and the input required to perform a calculation includes the respective state vectors, position error covariance matrices and physical sizes of objects involved.(3) Two methods to analyze relative trajectory safety between chaser and target are developed, which are 3-sigma ellipsoid based methodology and collision probability based methodology.

1分析了交会对接各阶段面临的主要轨迹安全威胁，阐述了被动和主动安全策略、目标器的交会对接控制区域等保证交会安全的措施；(2)基于概率思想发展了线性和非线性运动情况下飞行器与空间碎片的碰撞判断方法，提出采用总碰撞概率和拟最大瞬时碰撞概率来综合描述飞行器与空间碎片的碰撞危险程度，推导了通过飞行器和空间碎片各自的状态矢量、位置误差协方差矩阵以及形状尺寸来计算碰撞概率的公式；(3)提出了两种分析追踪器和目标器之间相对轨迹安全的新方法：基于3σ椭球的轨迹安全分析方法和基于碰撞概率的轨迹安全分析方法。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。