误差的均方

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。

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。

The simulation results demonstrate that the proposed algorithm can effectively reduce the location estimation error and variance of the MS, and has favorable performance in both root mean square error and mean error cumulative distribution function.

仿真结果表明，该算法能有效降低移动台位置估计的误差和方差，具有良好的均方根误差和均值误差CDF性能。

It is important to suitably estimate the root mean square of observation error in a given assimilation system.

在观测资料同化系统中，观测误差均方差与背景场误差均方差共同决定着观测信息与背景场信息的相对重要性以及这些信息在空间及不同变量间的扩展方式，故在资料同化系统中起到决定性作用。

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。

Four sub-channels are used in the forward equalizer and the coefficients of the equalizer are adjusted by the error of constant modulus algorithm. The advantages of FSE and DFE are integrated. The ideal equalization can be obtained as long as the length of the equalizer equal to or bigger than that of the channel, and the algorithm has the characteristics of faster convergence and smaller mean square error.

该算法前馈滤波器采用4路子信道系统模型，用常数模误差函数对均衡器权系数进行调整，综合了分数间隔均衡器和判决反馈均衡器的优点，均衡器权长只要大于或等于信道长度就能完全均衡信道，该算法收敛速度比波特间隔判决反馈盲均衡算法与T/4分数间隔盲均衡算法(T/4FSE)快、均方误差比BSDFE与T/4FSE小，且计算量不变，有利于信息的实时恢复。

The maximum error of regional anomaly separation is 3.101×10^(-6)m/s^2 the mean square error is 0.989×10^(-6)m/s^2 and the maximum percentage error is 7.76% for several data on the boundary and is lower than 4.1% for the other points.

分离出的区域异常最大误差为3.101×10^(-6)m/s^2，均方差为0.989×10^(-6)m/s^2，最大百分比误差仅在边部的几个数据上，为7.76%，其余各点的误差均小于4.1%。

During the search process,a lot of codewords can be rejected by utilizing the relationship among the sum of the input vector,the sums of the codewords and MSE.

在迭代过程中，利用输入矢量的和值、各码字的和值以及均方误差三者之间的各种特性排除大部分候选码字而免去许多均方误差计算。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。