On <i>F</i>-modelling-based empirical Bayes estimation of variances

Summary We consider the problem of empirical Bayes estimation multiple variances when provided with sample variances. Assuming an arbitrary prior on variances, we derive different versions estimators using loss functions. For one particular function, resulting estimator relies marginal cumulative distribution function only. When replacing it obtain version called $F$-modelling-based provide theoretical properties this estimator, and further demonstrate its advantages through extensive simulations real data analysis.