A class of general pretest estimators for the univariate normal mean
A class of general pretest estimators for the univariate normal mean
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DOI：
10.1080/03610926.2021.1955384
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
J. Shih;Yoshihiko Konno;Yuan-Tsung Chang;T. Emura
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文献类型：
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作者：
J. Shih;Yoshihiko Konno;Yuan-Tsung Chang;T. Emura
摘要本文提出了一元正态均值的一类一般预检验估计。所提出的类的主要数学思想是随机化测试的适应，其中随机化概率与收缩参数有关。因此，建议的类包括许多现有的估计，如预检验，收缩，贝叶斯和经验贝叶斯估计的特殊情况。此外，建议的类可以很容易地调整用户通过调整显着性水平和概率函数。我们推导出所提出的类的理论性质，如分布函数，偏差和MSE的表达式。我们的表达式的偏见和MSE原来是简单的比那些以前推导出的一些现有的公式的特殊情况。我们还进行了模拟研究，以检查我们的理论结果，并通过一个真实的数据集演示了所提出的类的应用。
Abstract In this paper, we propose a class of general pretest estimators for the univariate normal mean. The main mathematical idea of the proposed class is the adaptation of randomized tests, where the randomization probability is related to a shrinkage parameter. Consequently, the proposed class includes many existing estimators, such as the pretest, shrinkage, Bayes, and empirical Bayes estimators as special cases. Furthermore, the proposed class can be easily tuned for users by adjusting significance levels and probability function. We derive theoretical properties of the proposed class, such as the expressions for the distribution function, bias, and MSE. Our expressions for the bias and MSE turn out to be simpler than those previously derived for some existing formulas for special cases. We also conduct simulation studies to examine our theoretical results and demonstrate the application of the proposed class through a real dataset.