New development of statistical estimation of parameters with linear inequalities restriction

我们首先考虑估计两个有序方差未知的正态分布的共同均值的问题。我们给出了一大类估计量，其中包括Nair（1982）和Elfessi等人（1992）提出的估计量，并表明估计量随机支配不考虑方差顺序限制的估计量，包括Graybill和Deal（1959）给出的估计量。然后，我们提出了一类广义的两个有序均值在未知方差是有序的情况下的个体估计。我们表明，在估计具有较大方差的平均值时，不考虑方差的阶数限制的估计量随机地被考虑了两个阶数限制的估计量所支配。然而，在估计较小方差的均值方面，即使在均方误差方面也不可能有类似的改进。我们还给出了两个有序均值同时估计问题的支配结果。此外，本文还讨论了对这两个均值的无偏估计量的改进。本文还在Pitman接近准则下讨论了上述问题，并证实了Pitman接近准则的有效性。

We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959).Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators which take into account both order restrictions. However, in terms of estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is also discussed.We also discuss the above problems under Pitman closeness criterion and confirm the validity of Pitman closeness criterion.