THE ADMISSIBILITY OF NON-HOMOGENE OUS ESTIMATE OF VARIANCE IN LINEAR MODEL

Consider model Y=Xβ+e, where X_n×p is a design matrix, e₁,e₂,…,e_n, iid. withE（e_i）=E（e_i³）=0,E（e_i²）=σ²,E（e_i⁴）=3σ⁴,i=1,2,…,n. We discussed the problem about admissibility of the estimate of σ² in the class \mathscrQ=Y'AY+l'AY+f;Y'AY+l'AY+f≥0, for any Y. Here was offered a necessary and sufficient condition of admissibility if rank (X_n×p) =n; and we gave one complete class of \mathscrQ and a sufficient oondition under which the estimator was admissible if X_n×p=I.