On a two stage shrinkage testimator of the mean of a normal distribution
On a two stage shrinkage testimator of the mean of a normal distribution
复制标题
关于正态分布均值的两阶段收缩检验器
DOI：
10.1080/03610928408828802
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发表时间：
1984
影响因子：
0.8
通讯作者：
T. Raghunathan
中科院分区：
文献类型：
--
作者：
V. B. Waikar;F. J. Schuurmann;T. Raghunathan
令 X 呈正态分布，均值 μ 未知，方差 σ2 已知。此外，假设关于μ的先验知识可以以μ的初始估计μ0的形式获得。建议通过基于假设检验结果的检验器来估计未知平均值。如果基于大小为 n1 的第一个样本接受 H0，我们采用其中权重因子 k 是检验 H0 的检验统计量的函数。然而，如果 H0 被拒绝，我们将获得大小为 n2 的第二个样本，并取 。选择一个均方误差的表达式，并与单个样本均值的方差进行比较。还考虑了方差 σ2 未知的情况。
Let X be distributed normally with unknown mean μ and known variance σ2. Further, it is assumed that prior knowledge about μ is available in the form of an initial estimate μ0 of μ. It A is proposed to estimate the unknown mean by a testimator that is based upon the result of a test of the hypothesis If H0 is accepted based on the first sample of size n1 we take where the weighing factor k is a function of the test statistic for testing H0. However, if H0 is rejected, we obtain a second sample of size n2, and take . Choosing an expression for the mean square error of is derived and comparisons are made with variance of a single sample mean. The case when the variance σ2 is unknown is also considered.