增长曲线模型中协差阵的MINQE(U,NND)与UMVNNQUE

MINQE（U, NND） and UMVNNQUE of Covariance Matrix in Growth Curve Model

摘要: 本文对任给定的非负定阵C≠0,给出了Tr（C∑）的UMVNNQUE（一致最小方差非负二次无偏估计）存在的充要条件,证明了Tr（C∑）的UMVNNQUE存在的充要条件恰是Tr（C∑）的MINQE（U,NND）（最小模二次无偏非负估计）成为Tr（C∑）的UMVNNQUE的充要条件,且在UMVNNQUE存在时,具体给出了Tr（C∑）的UMVNNQUE,它恰是Tr（C∑）的MINQE（U,NND）。

Abstract: In this paper, for any given matrix C（0 ≠ C ≥ 0）, we consider the nonegative estimation of liner estimable function Tr（C∑） of the covariance matrix S, and obtain the n. s. condition for the MINQE（U, NND） of Tr（C∑）to be also its UMVNNQUE, and prove that it is exactly the n.s. condition for Tr(（C∑）’s UMVNNQUE to exist. Moreover, we give concretely Tr（C∑）’s UMVNNQUE （provided a UMVNNQUE exists）, it is just the MINQE（U.NND） of Tr（C∑）.