Gaussian Heteroskedastic Empirical Bayes without Independence
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In this note, we propose empirical Bayes methods under heteroskedastic Gaussian location models, without assuming that the unknown location parameters are independent from the known scale parameters. We derive the finite-sample convergence rate of the mean-squared error regret of our method. We also derive a minimax regret lower bound that matches the upper bound up to logarithmic factors. Moreover, we link decision objectives of other economic problems to mean-squared error control. We illustrate our method with a simulation calibrated to the Opportunity Atlas (Chetty, Friedman, Hendren, Jones and Porter, 2018) and Creating Moves to Opportunity (Bergman, Chetty, DeLuca, Hendren, Katz and Palmer, 2019).
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