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Arc-Sin Transformation for Binomial Sample Proportions in Small Area Estimation

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概要 The arc-sin transformation has long been used as a variance stabilizer for the binomial sample proportion arising out of binary data. The natural backtransformed function is useful for returning an es...timate 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 proportions 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 estimators and corresponding MSE estimators ourperform 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.続きを見る

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登録日 2024.04.02
更新日 2024.04.15