Precision of individual estimators in simultaneous estimation of parameters
Precision of individual estimators in simultaneous estimation of parameters
复制标题
参数同时估计中个体估计器的精度
DOI：
10.1093/biomet/65.1.23
复制
发表时间：
1978
期刊：
影响因子：
2.7
通讯作者：
Nobuo Shinozakt
中科院分区：
文献类型：
--
作者：
C. Rao;Nobuo Shinozakt
摘要对于向量参数的Stein型估计，得到了单个参数估计量的偏置和均方误差。我们知道，对于这样的估计量，其在估计的不同参数上的平均均方误差小于通常的无偏估计量。然而，对于相应参数的任何单个估计量的均方误差，这种性质可能不成立。研究发现，当用Stein型估计器同时估计多个参数时，一些估计器的均方误差比通常的无偏估计器大，而另一些估计器的均方误差则小。对于参数数量及其均值和标准差的几种组合，计算了Stein类型较好的参数值范围。
SUMMARY Biases and mean squared errors of estimators of individual parameters are obtained for Stein type estimators of a vector parameter. It is known that for such estimators the average mean squared error over the different parameters under estimation is smaller than that for the usual unbiased estimators. However, such a property may not hold for the mean squared error of any individual estimator for the corresponding parameter. It is found that when a number of parameters are estimated simultaneously by Stein type estimators, some individual estimators have larger mean squared error than those of the usual unbiased estimators and others less. For several combinations of number of parameters and their mean and standard deviation, the range of parameter values for which the Stein type is better has been computed.