生长曲线模型中几个相对效率

SOME RELATIVE EFFICIENCIES OF B IN GROWTH CURVE MODEL

对于一般生长曲线模型Ｙｑ×ｎ＝Ａｑ×ｎＢｍ×ｋＣｋ×ｎ＋ｅｑ×ｎ，Ｅ（ｅ）＝０，ｃｏｖｅ＝Ｖｎ×ｎΣｑ×ｑ的Ｂ的ＢＬＵＥＢ＝（ＡΣ－１Ａ）－１Ａ′Σ－１·ＹＶ－１Ｃ′（ＣＶ－１Ｃ′）－１，当用Ｂ的另一个估计Ｂ＝（Ａ′Ａ）－１Ａ′ＹＶ－１Ｃ′）－１代替Ｂ估计Ｂ时，将会产生差异，本文定义了４种衡量这种差异的尺度，称之为Ｂ对于Ｂ的相对效率。

For the general growth curve linear model, Y=ABC+e,E(e)=0, cov e=VΣ,B *(A′Σ -1 A) -1 A′Σ -1 YV -1 .C′(CV -1 C′) -1 is BLUE of B.B(A′A) -1 A′YV -1 C′(CV -1 C′) -1 is a linear unbiased estimate of B . In this article, four kinds of relative efficiencies of B (to B * ) are proposed and their upper bounds are given.