ARC-SIN TRANSFORMATION FOR BINOMIAL SAMPLE PROPORTIONS IN SMALL AREA ESTIMATION
ARC-SIN TRANSFORMATION FOR BINOMIAL SAMPLE PROPORTIONS IN SMALL AREA ESTIMATION
复制标题
DOI：
10.5705/ss.202020.0446
复制
发表时间：
2023-04-01
影响因子：
1.4
通讯作者：
Ghosh, Tamal
中科院分区：
文献类型：
--
作者：
Hirose, Masayo Y.;Ghosh, Malay;Ghosh, Tamal
反正弦变换长期以来一直被用作由二进制数据产生的二项样本比例的方差稳定器。自然反变换函数用于返回对感兴趣的参数的原始尺度的估计。然而，已知这样的变换在估计原始感兴趣参数时导致偏差。在这项研究中，我们找到了明确的渐近偏差调整经验贝叶斯（EB）估计的二项式样本比例的小区域估计的背景下。我们得到一个明确的二阶正确的近似的均方误差（MSE）的估计，以及这些MSE的二阶正确的估计。此外，所提出的EB估计和相应的MSE估计优于他们的竞争对手的偏差和方差，在模拟研究中所示。我们将我们的方法应用于日本每个都道府县与2019冠状病毒病（COVID-19）相关的真实的数据。
The arc-sin transformation has long been used as a variance stabilizer for the binomial sample proportion arising out of binary data. The natural back -transformed function is useful for returning an estimate to the original scale of the parameter of interest. However, it is known that such a transformation leads to bias when estimating the original parameter of interest. In this study, we find explicit asymptotic bias-adjusted empirical Bayes (EB) estimators for binomial sample pro-portions in the context of small area estimation. We obtain an explicit second-order correct approximation of the mean squared errors (MSEs) of such estimators, as well as second-order correct estimators of these MSEs. Moreover, the proposed EB esti-mators and corresponding MSE estimators outperform their competitors in terms of the bias and variance, as demonstrated in a simulation study. We apply our methodology to real data associated with Coronavirus Disease 2019 (COVID-19) for each prefecture in Japan.