Large-Scale Estimation under Unknown Heteroskedasticity

2025/07/03 by Ho, Sheng Chao
#Econometrics (econ.EM) #FOS: Economics and business

paper · doi:10.48550/arxiv.2507.02293

Abstract

This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of (log n)^κ/ n. The estimators are employed in a study of teachers' value-added, where we find that allowing for heterogeneous variances across teachers is crucial for delivery optimal estimates of teacher quality and detecting low-performing teachers.

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