最小

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。

And then some ellipses that AUGR estimator is better than the OLS estimator and AUGL estimator is better than the OLS estimator are given, respectively.Second, the definition of the almost unbiased unified biased estimator is proposed. This definition includes the familiar almost unbiased estimators in literatures, and it is the unified expression of the familiar almost unbiased estimators. Followed the biased and variance are compared of AUUB estimator and the unified biased estimator, respectively. AUUB estimator has smaller bias than UB estimator and the variance of AUUB estimator is between the variance of UB estimator and 4 times of the variance of UB estimator. Finally the properties of AUUB estimator are discussed. The conclusion is gained that there are parameters made AUUB estimator is better than OLS estimator in terms of their mean square error. The sufficient and necessary condition that AUUB estimator is admissible is given. The ellipse is given that AUUB estimator is

然后给出了几乎无偏统一有偏估计的定义，该定义包括了文献中常见的几乎无偏估计，实现了常见几乎无偏估计的统一表达式；接下来我们比较了几乎无偏统一有偏估计与统一有偏估计的偏度与方差，得出了几乎无偏统一有偏估计比统一有偏估计有较小的偏度，几乎无偏统一有偏估计的方差介于统一有偏估计的方差与统一有偏估计的方差的四倍之间的结论；最后我们对统一有偏估计的主要性质作了讨论，证明了存在参数K，S使得几乎无偏统一有偏估计在均方误差意义下优于最小二乘估计的结论，给出了几乎无偏统一有偏估计为可容许估计的充要条件，还给出了在均方误差阵意义下几乎无偏统一有偏估计优于最小二乘估计的椭球。

From an economic point of view, a solvent having a small minimum solvent flow is a better entrainer and should result in a lower cost design than a solvent having a large minimum solvent flow.

从经济的角度看，最小溶剂流量较小的溶剂比最小溶剂流量较大的溶剂成本低廉，是优良共溶剂。

The basic principle of least-squares method is to choose the model parameters minimizing model error sum of squares, thus the name "least squares method."

最小二乘法的基本原理是选择模型参数极小化模型误差平方和，因此而得名"最小二乘法"。

Airspace Image Fusion such as simple fusion method (pixel average, maximal or minimal pixel selection), Frequency-domain image fusion methods include the multiresolution image fusion techniques based on multi-scale pyramid decomposition, and the image fusion method based on wavelet transform Image Pre-processing like Filter processing (neighborhood average filter, median filtering method) and Image Registration.

首先介绍了图像信息融合的概念、优势、发展历史和应用领域，并介绍了图像融合的三个层次及常用的空域图像融合方法，空域融合方法有像素平均法、像素最大最小法、像素加权平均法，频域融合方法包括图像的多尺度分解、图像的小波变换、基于小波变换的图像融合方法。

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

Orthogonal least square is a widely used approach to training networks, so it also can be applied to wavelet networks.

正交最小二乘法是一种常用的前向神经网络训练方法，因此可以用正交最小二乘法训练小波网络。

Minimum mold areas for platen size should always be observed, even in minimum clamp situations.

我们经常看到的是安装尺寸较小的模具（接近最小的模具安装尺寸），然后用最小的合模力。

This new algorithm can derive a rheological parameter estimation that shows superior statistic features of fitting residual error unbiasedness and least variance.

该算法不需要人工给定迭代初始值，迭代过程稳定收敛到最小点，不会陷入极小点陷阱，收敛速度很快，所得到的流变参数估计具有拟合残差无偏性和方差最小的优良统计特征。

1Mm ~~ 500mm2024: 2.5mm ~ 300mm 5052:0.4 mm ~ 100mm2, copper alloys: brass, brass environmental protection the minimum diameter of 1.5mm, maximum diameter 120mm , copper, tungsten copper, bronze (high, medium and low, chromium bronze, phosphor bronze, aluminum-bronze, silicon bronze, manganese Bronze, tin bronze, wear-resistant copper, copper alloy, copper Cup with disabilities (including plate, rod, row, ribbons, sticks, pipes, lines), such as several varieties. 3, China imported stainless steel material (304 , 301,316,202, including plates, rods, line and belt, sticks, Pai, possession) and many other industrial raw materials, as well as titanium, titanium rods. 316 diameter of the smallest of imports of stainless steel wire 0.2mm , maximum diameter of 15mm.

1mm~~500mm2024：2.5mm~300mm 5052：0.4mm~100mm2、合金铜材：黄铜、环保黄铜（最小直径1.5mm，最大直径120mm、红铜、钨铜、铍青铜、铬青铜、磷青铜、铝青铜、硅青铜、锰青铜、锡青铜、耐磨铜、合金铜、杯士铜（其中包括板、棒、排、带、枝、管、线）等数种品种。3、国产进口不锈钢材料（304、301、316、202中包括板、棒、线、带、枝、排、管）等多种工业原材料，以及钛板、钛棒。316不锈钢线进口直径最小0.2mm，最大直径15mm。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。