椭球约束下等均值模型中联合估计的可容许性

Admissible simultaneous estimators with respect to restricted ellipsoidal parameter space

摘要: 考虑等均值模型Y=1nβ+ε,ε的前四阶矩和正态分布N(0,σ2V)相同,β和σ2是未知参数.在椭球约束H=(β,σ-1):nh2β2≤σ2下,给出了方差σ2和二阶原点矩β2+σ2在估计类T=Y’A Y:A≥0中以及一、二阶矩(β,σ2)和(β,β2+σ2)的同时估计(q’Y,Y’A Y)在估计类ГT=(q’Y,Y’A Y):q∈Rn,A≥0中是容许估计的充要条件.

Abstract: Consider the model Y=1nβ+ε,the first four moment ofis the same as N(0,σ2V).The necessary and sufficient condition that Y’AY is admissible for variance and 2-oder origin moment β2+σ2,and that(l’Y,Y’AY is admissible for moments of order 1 and 2(β,σ2) and(β,β2+σ2) with respect to restricted ellipsoidal parameter space,is given.