The authors consider the problem of estimating the ordered means of two normal distributions with unknown ordered variances. The authors discuss the estimation of two ordered means, individually, in terms of stochasti...The authors consider the problem of estimating the ordered means of two normal distributions with unknown ordered variances. The authors discuss the estimation of two ordered means, individually, in terms of stochastic domination and MSE （mean squared error）. The authors show that in estimating the mean with larger variance, the usual estimator under order restriction on means can be improved upon. However, in estimating the mean with smaller variance, the usual estimator can＇t be improved upon even under MSE. The authors also discuss simultaneous estimation problem of two ordered means when unknown variances are ordered.展开更多
For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be...For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.展开更多
文摘The authors consider the problem of estimating the ordered means of two normal distributions with unknown ordered variances. The authors discuss the estimation of two ordered means, individually, in terms of stochastic domination and MSE （mean squared error）. The authors show that in estimating the mean with larger variance, the usual estimator under order restriction on means can be improved upon. However, in estimating the mean with smaller variance, the usual estimator can＇t be improved upon even under MSE. The authors also discuss simultaneous estimation problem of two ordered means when unknown variances are ordered.
文摘For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.
