OnF-modelling-based empirical Bayes estimation of variances
研究了在给定样本方差时，利用经验贝叶斯方法估计多个方差的问题，推导了不同损失函数下的贝叶斯估计量，并提出了基于F建模的经验贝叶斯估计量，通过模拟和实际数据验证了其优势。
Summary We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss functions. For one particular loss function, the resulting Bayes estimator relies on the marginal cumulative distribution function of the sample variances only. When replacing it with the empirical distribution function, we obtain an empirical Bayes version called the $F$-modelling-based empirical Bayes estimator of variances. We provide theoretical properties of this estimator, and further demonstrate its advantages through extensive simulations and real data analysis.