增长曲线模型方差扰动的局部影响分析

LOCAL INFLUENCE ANALYSIS OF VARIANCE PERTUBATION IN A GROWTH CURVE MODEL

考虑增长曲线模型Ｙ＝ＸＢＺ＋ε，ε～Ｎ（０，ＶｎΣｐ，其中Ｙ是ｐ×ｎ阶观察矩阵，Ｘ和Ｚ分别是ｐ×ｍ和ｒ×ｎ阶设计矩阵，Ｂ是ｍ×ｒ阶未知参数阵，Ｖｎ＞０，Σｐ＞０已知，分别是Ｙ的行向量和列向量的公共协方差矩阵；本文用矩阵微商法的思想，讨论了Ｖｎ和Σｐ单独和同时发生扰动时，对未知参数阵Ｂ在ｔｒａｃｅ意义下的最小二乘估计＾Ｂ的影响，给出了相应的影响度量；同时，对于Ｖｎ和Σｐ是某种特殊扰动（如单点扰动）的情形也作了讨论。文章最后一节的实例分析说明了本文给出的局部影响分析是行之有效的。

For the growth curve model with general known variance structure: Y=XBZ+ε,ε～N(0,VΣ) ,where Y and ε are random matrices, B is an unknown parameter matrix, X and Z are known matrices, V and Σ are known variance matrices (V>0,Σ>0) ,the paper considered the effects of small change of the error variance matrix on the L.S.E.of B,and presented a method called matrix derivative method to measure the local influence of observation. We also obtained the influential measurement under a special structure of V and Σ Furthermore,an approach for detecting influential observation is given.