The Tweedie Oracle and Regret Bounds in Empirical Bayes Methods

Written by lossfunctiontech | Published 2025/09/10
Tech Story Tags: loss-function | empirical-bayes | regret-analysis | tweedie-oracle | statistical-learning | minimax-estimation | mixing-distributions | nonparametric-methods

TLDRThis article explores the concept of regret in empirical Bayes, specifically in the context of the Tweedie oracle rule.via the TL;DR App

Table of Links

Abstract and 1. Introduction

  1. The Compound Decision Paradigm
  2. Parametric Priors
  3. Nonparametric Prior Estimation
  4. Empirical Bayes Methods for Discrete Data
  5. Empirical Bayes Methods for Panel Data
  6. Conclusion

Appendix A. Tweedie’s Formula

Appendix B. Predictive Distribution Comparison

References

Appendix A. Tweedie’s Formula

Robbins (1956) attributes Proposition 2 to Tweedie (1947). It follows by straightforward exponential family computations, as in van Houwelingen and Stijnen (1983),

Differentiating again,

implies that δ must be monotone.

Authors:

(1) Roger Koenker;

(2) Jiaying Gu.


This paper is available on arxiv under CC BY 4.0 DEED license.


Written by lossfunctiontech | Loss Function fuels the quest for accuracy, driving models to minimize errors and maximize their predictive prowess!
Published by HackerNoon on 2025/09/10