We make the following assumption for when 2 is positive definite matrix, different estimators about matrix of regression coefficients and inefficiency of least squares estimate have been discussed in many documents . considered 2 is nonnegative definite matrix, this thesis derives best linear unbiased estimate of parameter matrix b and estimable parameter function kbl under the meaning of matrix nonnegative definite and the property of maximum probability of blue is investigated . next, we discuss some necessary and sufficient conditions of the equality of the lse and blue, then we derive the estimation of the deviation bet-ween the least squares and the best linear unbias estimators of the mean matrix, meanwhile a relative efficiency of lse ofb is proposed and its bound is given 当0时,众多文献讨论了回归系数阵的各种估计及lse的有效性,本文考虑了当0的情形,给出了回归系数阵b及其可估参数函数kbl的在矩阵非负定意义下的最优估计(blue),研究了它的一个最大概率性质,并且讨论了最小二乘估计成为最佳线性无偏估计的充分必要条件,在此基础上给出了均值矩阵的最小二乘估计与blue的偏差估计,定义了lse相对于blue的一个相对效率,并给出了它的界。
However, two-stage estimates of regression coefficients corresponding to these two estimates have approximate equal mean square error . for testing linear hypothesis about regression coefficients, banerjee and magnus ( 1997 ) studied the sensitivity of f-test sta, tistic ( fgls ( ) ) based on generalized least square estimate caused by variance parameter in general case and proposed sensitivity statistic and its distribution 关于回归系数的线性假设检验问题,banerjee和magnus(1997)在一般情况下从理论上研究了方差参数对基于广义最小二乘估计的f-检验统计量(f_(gls)())的种种影响,提出了敏感性的概念,并给出敏感统计量的形式及其分布。
However, two-stage estimates of regression coefficients corresponding to these two estimates have approximate equal mean square error . for testing linear hypothesis about regression coefficients, banerjee and magnus ( 1997 ) studied the sensitivity of f-test sta, tistic ( fgls ( ) ) based on generalized least square estimate caused by variance parameter in general case and proposed sensitivity statistic and its distribution 关于回归系数的线性假设检验问题,banerjee和magnus(1997)在一般情况下从理论上研究了方差参数对基于广义最小二乘估计的f-检验统计量(f_(gls)())的种种影响,提出了敏感性的概念,并给出敏感统计量的形式及其分布。
The present paper gives some profound results of linear biased estimation of regression coefficients which include linear biased estimation for the minimum mean square error, the necessary and sufficient conditions for the linear biased estimation superior to least square estimation, the necessary and suffic ) ent conditions for the admissibility of linear biased estimation and some linear biased estimators not included in the literatures 摘要给出回归系数的最小均方误差线性有偏估计、线性有偏估计优于最小二乘估计的充要条件及线性有偏估计为可容许估计的充要条件,同时给出文献中未涉及的一些有偏估计。
After synthetically analyses and researches of the existing methods for injection allocation rate, this article takes the group of water-injecting wells in waterflood oilfield as the research unit, the multiple regression method to decide the injection allocation rate is applied, by which and its regression coefficient and partial correlation coefficient, the multivariate regression models of model and model are developed 在对目前存在的配注方法的综合分析和研究之后,提出以水驱油田注水井井组为研究单元,采用多无回归方法来确定注水井井组配注量,并基于多元回归方法的回归系数和偏相关系数,分别建立了多元回归模型、。
In this dissertation, on the basis of comprehensive review of the study achievements on sediment transport, we get the fact that most of formula in sediment incipient motion and bed-load transport rate are established by classical regression analysis model, i . e . firstly establishing the formula according to related sediment transport theory, secondly computation for regression coefficients in formula by using field or laboratory experiment data 故本文在回顾并总结泥沙输移研究成果的基础上,指出大多数泥沙起动公式和输沙率公式的推求是采用传统回归模型,即先根据输沙理论定出计算公式,再用实测资料或试验数据率定公式系数。