均方误差

Finishing calculation of mean value, standard deviation, skewness, kurtosis of Beta distribution.(2) Fitting parameters of many kinds of typical distribution and using residual deviation to evaluate fitting precision.(3) Using Beta distribution as an agreed indication distribution applied to many kinds of practical photoelectric measurement distributions.(4) Deriving theory formula of Bayes point estimation about Beta distribution parameters and mean value and standard deviation on the condition of mean square error loss function and supposed the prior distribution is uniform distribution.(5) Generating MCMC sample from post distribution by the method of Gibbs sample algorithm. Calculating bayes point estimation from sample on the condition of mean square error loss function. Calculating confidence interval by an approximate method to complete interval estimation.

本文的主要工作有：(1)解决了Beta分布参数a和b的精确计算以及均值、标准差、偏度、峰度的计算问题；(2)拟合出10余种典型分布的Beta分布的两个参数，并且采用剩余标准差评价该Beta分布的拟合精度；(3)对多种典型的光学与光电测量系统的测量分布进行了Beta分布统示表示；(4)在假设先验分布为均匀分布前提下，得到参数a和b以及均值μ和标准差σ在均方误差损失函数下的贝叶斯点估计理论计算公式；(5)利用直接抽样的Gibbs抽样算法，从后验分布中产生MCMC样本，从样本直接计算均方误差损失函数下的贝叶斯点估计，并使用一种近似方法计算其置信区间，完成区间估计。

In the fifth chapter, we propose the conditional generalized ridge-type estimator of regression coefficient in restricted linear regression model, and prove that it is superior to the restricted best linear unbiased estimator in terms of mean squares error and mean squares error matrix, we also give the choice of parameters matrix K.

第五章给出了约束线性回归模型中回归系数的条件广义岭估计，讨论了它的优良性，证明了它在均方误差及均方误差矩阵下都优于约束最小二乘估计，并给出了参数矩阵K的选择。

In this paper, we study characterizations of admissible in the general linear model Y, Xβ,ε|ε～(0,σ~2∑. We demonstrate that an admissible linear estimator is as the conditional generalized ridge-type estimation in the no constraint, equality constraint, inequality constraint general linear model. We study the superiority of this conditional generalized ridge-type estimation, and prove that it is superior to the restricted best linear unbiased estimator in terms of mean squares. We also give the choice of the matrix K.

本文主要研究了一般线性模型Y，Xβ，ε|ε～(0，σ~2∑中参数估计的可容许性特征，得到了一般线性模型在无约束，有等式约束及有不等式约束下，可容许线性估计均具有条件广义岭估计的形式的结论，并且讨论了这一条件广义岭估计的优良性，证明了其在均方误差和均方误差矩阵意义下都优于约束最小二乘估计，给出了参数矩阵K的选取方法。

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。

Coefficient distribution of the APIDCSF is similar to that of circular quincunx Neville filter and its interpolating performance outperforms the Neville filters with high orders vanishing moments.The aim of bidimensional interpolating is to diminish the error between the true value and the estimated one.

二维内插的质量是以预测值与真值之间的误差来衡量的，按照最小均方误差的准则，利用二维自相关函数模型和环形内插滤波器的系数分布特点构造了最小均方误差意义上的环形最优内插器，实验证明了全相位离散反余弦内插器近似于最优内插器。

Third, the discussion of the corresponding relationship of the real angles to the apparent real angles is performed, the asymptotic bias and MSE of real angles are given. Fourth, based on above conclusions, the analysis of two typical cases is made by numerical analysis and computer simulation: Case A when the impinging signals are divided into desired signals and interfering signals: it is shown that similar to Cyclic estimation of DOA, the smaller the separation between interfering direction and signal direction, in general, the smaller the estimation variance.

首先，研究了无穷快拍时信号数目有误的最大似然估计，引入了视在真实角度的概念；其次，导出了视在真实角度最大似然估计大样本时的分布以及渐近均方误差的解析表达式，而且还证明了：Stoica性能分析结果是现在的分析结果在信号数目准确时的特例；第三，讨论了真实角度与视在真实角度的关系，给出了真实角度的渐近偏和渐近均方误差；第四，依据前面的结果，利用数值分析和模拟实验的方法对两种典型情况做了分析： 1 在入射信号被分为干扰信号和所需信号情况下：结果表明：与CyclicDOA估计一样，干扰方向与所需信号方向靠的越近，所需信号估计的方差越小，越远离，方差越大。

At the same time, there are a lot of criterions, such as: mean squared errors criterion, generalized mean squared errors criterion and Pitman criterion.

不同方法的出现就必然会引出优劣比较问题，相应的也就出现了一些比较不同估计的判别准则，如：均方误差准则、广义均方误差准则以及pitman 准则等。

Based on the normalized mean square error,an instrumental variable is derived for yielding a variable clipping function to provide fast convergence and small mean square error.

基于归一化的均方误差，引入了一个辅助变量，导出了时变限幅函数，加速了收敛并且得到了更小的均方误差。

In this paper, the bias of the ratio estimator and the estimateof mean square errors of this estimator with known numerator have been compared and discussed.

给出了分子已知情况下比率估计量的偏差和均方误差以及均方误差的估计，并对两类比率估计量进行了比较。

Second,a new estimator called generalized rootpower estimator of regression coefficients in growth curve model is obtained.For the newestimator,its superiority over the LS estimator and the root power estimator,and its admissibilityare proved.Two methods,two kinds of arithmetic of choosing the generalized root powerparameters are introduced.A demonstrative practical example is provided.

对增长曲线模型中的回归系数矩阵提出了一种新的估计——广义根方估计，并证明了通过广义根方偏参数的适当选取可使得该估计在均方误差和均方误差矩阵的意义下优于已有的最小二乘估计估计和根方估计；及证明了广义根方估计是可容许估计；还给出了选取广义根方偏参数的两种方法、算法和应用实例。

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。