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

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,σ2):nh-1β2≤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.

Consider the model Y = lnβ ＋ε , the first four moment ofis the same as N（O, 2 V）. The necessary and sufficient condition that Y′A Y is admissible for variance and 2 - oder origin moment β2 ＋σ^2, and that （l′ Y, Y′A Y is admissible for moments of order 1 and 2 （β,σ^2） and （β,β2 ＋σ^2） with respect to restricted ellipsoidal parameter space,is given.