锥序约束下两个指数总体均值的估计

Estimation of Two Sample Exponential Distributions under Cone Restriction

讨论样本容量相等时 ,在锥序约束 a1λ1≤λ2 ≤a2 λ1条件下 ,两个指数总体均值 λi( i=1 ,2 )的估计量 .证明约束极大似然估计 λi 具有比经典极大似然估计 Xi 更小的均方误差 ,并且讨论 λi 对 Xi的功效 e( λi,Xi) ,i=1 ,2 .

The present paper deals with the estimation of the means of two sample exponential distributions, with the same sample size, under cone restriction a 1λ 1≤λ 2≤a 2λ 1, with a 1,a 2>0. It is proved that the restricted maximum likelihood estimators (RMLE) have less mean square errors than the usual sample means, and the efficiency of the RMLE with respect to sample means is discussed.