Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are...Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.展开更多
In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovest...In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.展开更多
For a seemingly Unrelated regression system with the assumption of normality,a necessary and sufficient condition for the existence of the Uniformly Minimum Risk Unbiased (UMRU)estimator of regression coefficients und...For a seemingly Unrelated regression system with the assumption of normality,a necessary and sufficient condition for the existence of the Uniformly Minimum Risk Unbiased (UMRU)estimator of regression coefficients under strictly convex loss is obtained;it is proved that any unbiased estimator can not improve the least squares estimator;it is also shown that no UMRU estimator exists under missing observations.展开更多
In this article, the Bayes linear unbiased estimator （BALUE） of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator （LSE） is studied in terms of...In this article, the Bayes linear unbiased estimator （BALUE） of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator （LSE） is studied in terms of the mean square error matrix （MSEM） criterion and Bayesian Pitman closeness （PC） criterion.展开更多
为了减小到达时间差(time difference of arrival,TDOA)方法在定位过程中存在的系统测量噪声和非视距误差,提出了一种基于最优线性无偏估计的TDOA定位算法。该方法首先利用Chan算法计算定位初始位置,在初始位置处泰勒级数展开得到位置...为了减小到达时间差(time difference of arrival,TDOA)方法在定位过程中存在的系统测量噪声和非视距误差,提出了一种基于最优线性无偏估计的TDOA定位算法。该方法首先利用Chan算法计算定位初始位置,在初始位置处泰勒级数展开得到位置估计量的线性模型,并求取误差加权矩阵、系数矩阵及协方差矩阵等参数;然后采用加权最小二乘法对最终位置进行最优无偏估计,同时推导出定位误差的最小方差阵。仿真实验结果表明,在相同环境下该算法的定位精度优于Chan和Taylor算法,同时显著减小了算法的运算量。展开更多
文摘Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.
基金Supported by China Mathematics Tian Yuan Youth Foundation (10226024) and China Postdoctoral Science Foundation.
文摘In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.
基金Supported by the National Natural Science Foundation of China.
文摘For a seemingly Unrelated regression system with the assumption of normality,a necessary and sufficient condition for the existence of the Uniformly Minimum Risk Unbiased (UMRU)estimator of regression coefficients under strictly convex loss is obtained;it is proved that any unbiased estimator can not improve the least squares estimator;it is also shown that no UMRU estimator exists under missing observations.
基金Supported by the National Natural Science Foundation of China (No.10801123,10801124,10771204)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KJCX3-SYW-S02)
文摘In this article, the Bayes linear unbiased estimator （BALUE） of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator （LSE） is studied in terms of the mean square error matrix （MSEM） criterion and Bayesian Pitman closeness （PC） criterion.
文摘为了减小到达时间差(time difference of arrival,TDOA)方法在定位过程中存在的系统测量噪声和非视距误差,提出了一种基于最优线性无偏估计的TDOA定位算法。该方法首先利用Chan算法计算定位初始位置,在初始位置处泰勒级数展开得到位置估计量的线性模型,并求取误差加权矩阵、系数矩阵及协方差矩阵等参数;然后采用加权最小二乘法对最终位置进行最优无偏估计,同时推导出定位误差的最小方差阵。仿真实验结果表明,在相同环境下该算法的定位精度优于Chan和Taylor算法,同时显著减小了算法的运算量。
