Nonparametric Empirical Bayes Estimation on Heterogeneous Data

Understand

The simultaneous estimation of many parameters based on data collected from corresponding studies is a key research problem that has received renewed attention in the high-dimensional setting.

• Many practical situations involve heterogeneous data where heterogeneity is captured by a nuisance parameter.
• Effectively pooling information across samples while correctly accounting for heterogeneity presents a significant challenge in large-scale estimation problems.
• We address this issue by introducing the ``Nonparametric Empirical Bayes Structural Tweedie" (NEST) estimator, which efficiently estimates the unknown effect sizes and properly adjusts for heterogeneity via a generalized version of Tweedie's formula.