Empirical Bayes mean estimation with nonparametric errors via order statistic regression on replicated data

We study empirical Bayes estimation of the effect sizes N units from K noisy observations on each unit. show that it is possible to achieve near-Bayes optimal mean squared error, without any assumptions or knowledge about size distribution noise. The noise can be heteroscedastic and vary arbitrarily unit Our proposal, which we call Aurora, leverages replication inherent in per recasts problem as a general regression problem. Aurora with linear provably matches performance wide array estimators including sample mean, trimmed median, well James-Stein shrunk versions thereof. automates for Internet-scale datasets, demonstrate data large technology firm.