Research On The Admissible Quadratic Error Variance Estimations In Growth Curve Model, And On The Admissibility Of Quadratic Estimations With Restricted Parameter Sets

Admissibility of estimations has gained more attention since 1940's. For linear model, the important thing is the admissible estimations of the unknown regression coefficients and error variance. The admissibility of quadratic estimations of error variance in linear model was first put forward by Wu Qiguang,Cheng Ping and Li Guoying, and after a few years'study,perfect results were obtained.This paper studies the admissible quadratic error variance estimations in growth curve model, which has many applications. The growth curve model is as following: When p=1, growth curve model is linear model.Therefore, growth curve model is a generalization of linear model, it was introduced in 1938 to research on the different groups in the growth of plants and animals.For this model, under the assumption:H0:G=In,rank(A)= r0,tr[(ABC)'(ABC)]≤σ2} Under the assumption H2:G=In,rank(A)=r< n,rank(C)-p and hypotheses H3:G=In,A=1n,C=1p, discusses the admissibility of quadratic estimations tr(Y'MY) of error variance in the class D={tr(Y'MY):Mn×n>0}, respectively.