推广的生长曲线模型的未知参数矩阵的两步估计

The Two stage Estimate on the Unknown Parameter Matrices in the Extension of the Growth Curve Model

生长曲线模型 (growthcurvemodel,简记为GC)是在研究生物的某指标随时间的增长而变化建立的一种模型 ,本研究在V >0未知的情况下 ,得到了推广的生长曲线模型未知参数矩阵的两步估计 。

Consider the extension on the growth gurve model Y=∑X\-iθ\-iM\+′\-i+ε,EY=∑ti=1X\-iθ\-iM\+′\-i,D(Y)=D()=I\-nV ,where, Y:n×p, and ε:n×p are random matrices; X\-i:n×m\-i and M\-i:p×q\-1 , are known designed matrices; θ\-i:m\-i×q\-i are unknown parameter matrices, i=1,2,…,t, V:p×p is and unknown variance matrix of ε . Firstly, the estimate of V is given out, then, the estimated of (θ\-1θ\-2) is attained, and showed it be an unbiased estimate of (θ\-1θ\-2) .\;