增长曲线模型均值矩阵的一种新的相对效率  

The New Relative Efficiency of Mean Matrix in Growth Curve Model

作　　者：胡桂开[1] 彭萍[1] 吴志强[1] 

机构地区：[1]东华理工学院数学与信息科学学院,江西抚州344000

出　　处：《东华理工学院学报》2006年第4期394-396,共3页Journal of East China Institute of Technology

基　　金：东华理工学院院长基金(DHYK0613)

摘　　要：对于一般增长曲线模型,当设计阵和协方差阵满足一定的条件时,均值矩阵(XBZ)的最小二乘估计(LSE)与最佳线性无偏估计(BLUE)相等,可用LSE代替BLUE。当这些条件不满足时,用LSE代替BLUE就要蒙受一些损失,有时这种损失很大,因而研究这种损失的大小显得相当重要,通常用它们协方差阵的差异来度量,从不同的准则出发,可以定义不同的相对效率,利用广义行列式定义了一种新的相对效率,并给出了它们的下界。When the design matrix and covariance matrix are sufficient to certain condition for the general growth curve linear model, the least square estimate（LSE） of mean matrix（XBZ） equals the best linear unbiased estimate （BLUE） of it. So we can substitute LSE for. But when these conditions are not satisfied, the substituting leads to some loss. Sometimes the loss is very large, therefore it is important for us to study the size of the loss. Generally the difference of their covariance is use to measure the loss, we can define different relative efficiency according to the distinct criterion. This paper brings forward a new kind of relative efficiency of LSE of XbZ （ to the BLUE of LSE） and attains its lower bound. Key Words：

关 键 词：增长曲线模 相对效率 最小二乘估计 

分 类 号：O151.21[理学—数学]