误差的均方

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。

The relation between mean square error and the characteristics of the measurement system is derived.

推导了动态测量的均方误差与测量信号和仪器特性的关系，明确了动态测量误差的各种成分，动态测量误差与静态测量误差的区别及联系。

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。

Prediction results of indepe ndent and dependent samples show that the RMS errors of SSTA predicted in 10～12 months ahead are smaller than SSTA mean square deviation and that the relative e rrors in 5 months ahead are less than 50%.

经检验，对于非独立和独立样本，预报的均方根误差分别在12个月和1 0个月预报时效内小于SSTA的均方差，相对误差在5个月预报时效内都小于50％。

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。

Some improvements for the mean square errors of the ratio estimator are presented.

改进了比率估计的均方误差，给出了偏差的价为 1/n3 的比率估计量均方误差及其估

The mean square errors and estimated mean square errors for the ratio estimator with bias of order 1/n 3are given.

改进了比率估计的均方误差，给出了偏差的价为 1/n3 的比率估计量均方误差及其估

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。

A necessary and sufficient condition for the unbiasedness of Balanced LS Estimation is gained, and for the given L, t can be chosen to make the MSEM of the Balanced LS Estimation less than that of OLS Estimation.

给出了平衡LS估计为无偏估计的充分必要条件，对于给定的L，适当地选择参数t可使平衡LS估计的均方误差矩阵小于OLS估计的均方误差矩阵。

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。